Ultimate CEE Master Question Bank: Physics - Mechanics

Section 1: Physical Quantities, Units, and Dimensions (1-15)

1. Which of the following is a fundamental physical quantity in the SI system?
(a) Velocity (b) Force (c) Electric Current (d) Energy

The dimensional formula for Force is:

(a) [MLT⁻¹] (b) [MLT⁻²] (c) [ML²T⁻²] (d) [ML⁻¹T⁻²]

The dimensional formula for Angular Momentum is the same as that for:
(a) Work (b) Power (c) Torque (d) Planck's Constant

The SI unit of pressure is the Pascal (Pa), which is equivalent to:

(a) N m (b) N m⁻¹ (c) N m² (d) N m⁻²

If the units of mass, length, and time are doubled, the unit of Force will become:
(a) Doubled (b) Halved (c) Four times (d) Unchanged

Which of the following pairs of physical quantities have the same dimensions?
(a) Work and Power (b) Momentum and Impulse (c) Pressure and Stress (d) Both b and c

The principle of homogeneity of dimensions states that:

(a) All physical quantities have dimensions.
b) An equation is dimensionally correct if the dimensions of all the terms on both sides are the
same.
c) Only quantities with the same dimensions can be added or subtracted.
d) Both b and c are correct.

The dimensional formula for the universal gravitational constant (G) is:
(a) [M⁻¹L³T⁻²] (b) [ML²T⁻²] (c) [MLT⁻²] (d) [M⁻¹L²T⁻²]

The number of significant figures in 0.005060 is:

(a) 3 (b) 4 (c) 6 (d) 7

A physical quantity that has both magnitude and direction but does NOT obey the laws of vector
addition is a:
(a) Vector (b) Scalar (c) Tensor (d) Phasor
(Note: Electric current is the classic example)

The dimensions of Planck's constant (h) are:

(a) [ML²T⁻³] (b) [MLT⁻¹] (c) [ML²T⁻¹] (d) [ML²T⁻²]

"Parsec" is a unit of:

(a) Time (b) Angle (c) Distance (d) Energy

The dimensional formula [ML²T⁻³] represents:

(a) Work (b) Torque (c) Power (d) Momentum

The percentage error in the measurement of mass and speed are 2% and 3% respectively. The
maximum percentage error in the estimation of kinetic energy (½mv²) is:
(a) 5% (b) 1% (c) 8% (d) 11%

Which of the following physical quantities is dimensionless?

(a) Refractive index (b) Strain (c) Relative density (d) All of the above

Section 2: Vectors (16-30)

1. Which of the following is a scalar quantity?
(a) Displacement (b) Electric Field (c) Acceleration (d) Electric Potential
 If the resultant of two vectors is zero, the two vectors must be:
(a) Equal in magnitude and in the same direction.
b) Equal in magnitude and in opposite directions.
c) Unequal in magnitude and in opposite directions.
d) Perpendicular to each other.

The dot product (scalar product) of two perpendicular vectors is:

(a) 1 (b) -1 (c) Zero (d) Their vector product

The cross product (vector product) of two parallel vectors is:

(a) 1 (b) -1 (c) A null vector (zero) (d) The dot product

If A . B = |A x B|, then the angle between vectors A and B is:

(a) 0° (b) 45° (c) 90° (d) 180°

The magnitude of the resultant of two forces of 3 N and 4 N acting at a right angle to each other
is:
(a) 1 N (b) 5 N (c) 7 N (d) 12 N

A unit vector is a vector that has a magnitude of ________ and points in a ________.
a) one; specific direction
b) zero; any direction
c) one; any direction
d) ten; specific direction

The area of a parallelogram formed by two adjacent vectors A and B is given by:
(a) A . B (b) |A x B| (c) A + B (d) ½ |A x B|

The work done by a force F causing a displacement d is given by the scalar product W = F . d. This
implies work is a:
(a) Scalar quantity (b) Vector quantity (c) Neither scalar nor vector (d) Sometimes scalar,
sometimes vector

A particle moves from a point (2, 3, 5) to a point (3, 4, 1). The displacement vector is:
(a) i + j + 4k (b) i + j - 4k (c) 5i + 7j + 6k (d) -i - j + 4k

The minimum number of unequal coplanar vectors whose sum can be zero is:
(a) 1 (b) 2 (c) 3 (d) 4

If A = 2i + 3j and B = -3i + 2j, the angle between them is:

(a) 0° (b) 45° (c) 90° (d) 180°

The vector product of two vectors is always:

(a) Parallel to the plane containing the two vectors.
b) Perpendicular to the plane containing the two vectors.
c) A scalar quantity.
d) In the same direction as the first vector.

A null or zero vector is a vector with:

(a) Zero magnitude and a specific direction.
b) Zero magnitude and an arbitrary direction.
c) Unit magnitude and an arbitrary direction.
d) Zero magnitude and no direction.

The resolution of a vector into components is the process of:

(a) Finding its magnitude.
b) Finding its direction.
c) Splitting it into two or more vectors whose sum is the original vector.
d) Multiplying it by a scalar.

Section 3: Kinematics (31-65)

1. A body starts from rest and moves with a uniform acceleration of 2 m/s². The distance covered
by the body in 5 seconds is:
(a) 10 m (b) 25 m (c) 50 m (d) 100 m

The slope of a distance-time (s-t) graph represents the:

(a) Acceleration (b) Speed/Velocity (c) Displacement (d) Time

The area under a velocity-time (v-t) graph represents the:

(a) Instantaneous velocity (b) Average velocity (c) Acceleration (d) Displacement

For a body thrown vertically upwards, the velocity at the maximum height is ________, and the
acceleration is ________.
a) maximum; zero (b) zero; g (downwards) (c) zero; zero (d) minimum; g (upwards)

A projectile is fired at an angle θ with the horizontal. Its trajectory is a:

(a) Straight line (b) Circle (c) Ellipse (d) Parabola

The horizontal range of a projectile is maximum when the angle of projection is:
(a) 30° (b) 45° (c) 60° (d) 90°

A body is projected at angles 30° and 60° with the same initial velocity. The ratio of their
horizontal ranges will be:
(a) 1:1 (b) 1:√3 (c) √3:1 (d) 1:2

In uniform circular motion, which of the following physical quantities remains constant?
(a) Velocity (b) Acceleration (c) Speed (d) Momentum

The acceleration directed towards the center of the circle in uniform circular motion is called:
(a) Tangential acceleration (b) Centripetal acceleration (c) Angular acceleration (d) Linear
acceleration

Two bodies are dropped from the same height. If one is twice as heavy as the other, they will
reach the ground (neglecting air resistance):
(a) Simultaneously (b) The heavier one first (c) The lighter one first (d) Depends on their shape

A car travels the first half of a distance with speed v₁ and the second half with speed v₂. The
average speed is:
(a) (v₁+v₂)/2 (b) 2v₁v₂/(v₁+v₂) (c) √(v₁v₂) (d) (v₂-v₁)/2

The instantaneous velocity of a particle is the:

(a) Average velocity over a long time interval.
b) Velocity at a particular instant of time.
c) Total distance divided by total time.
d) Rate of change of acceleration.

Which of the following is an example of one-dimensional motion?

(a) A car moving on a circular track.
b) A ball thrown into the air.
c) A train moving on a straight track.
d) The motion of the Earth around the Sun.

A ball is thrown upwards. The magnitude of its acceleration during the upward journey is:
(a) g (b) 0 (c) -g (d) Increasing

The horizontal component of a projectile's velocity during its flight (neglecting air resistance) is:
(a) Constantly increasing (b) Constantly decreasing (c) Constant (d) Zero at the highest point

The time of flight of a projectile is the time for which it remains in the air. For a given initial
velocity, it is maximum when the angle of projection is:
(a) 30° (b) 45° (c) 60° (d) 90°

Relative velocity of object A with respect to object B is given by:

(a) V_AB = V_A + V_B (b) V_AB = V_A - V_B (c) V_AB = V_B - V_A (d) V_AB = √(V_A² + V_B²)

A man walking east with a speed of 3 km/h encounters rain falling vertically with a speed of 4
km/h. He should hold his umbrella at an angle θ with the vertical such that tan(θ) is:
(a) 3/4 (b) 4/3 (c) 3/5 (d) 4/5

The slope of a velocity-time (v-t) graph represents the:

(a) Speed (b) Displacement (c) Acceleration (d) Time

If the velocity of a particle is given by v = At + B, the particle is moving with:

(a) Constant velocity (b) Constant acceleration (c) Variable acceleration (d) Constant
displacement

An object is in uniform motion if it travels:

(a) In a straight line. (b) With constant acceleration. (c) Equal distances in equal intervals of time.
(d) In a circular path.

The equations of motion (v = u + at, etc.) are valid only for motion with:
(a) Uniform velocity (b) Uniform acceleration (c) Variable acceleration (d) Circular motion

A body is dropped from a height H. The time it takes to reach the ground is proportional to:
(a) H (b) H² (c) 1/√H (d) √H

The maximum height attained by a projectile is given by H = u²sin²(θ)/2g. It is maximum when θ

is:
(a) 30° (b) 45° (c) 60° (d) 90°

A person in a moving train throws a ball vertically upwards. The ball will return to:
(a) The person's hands if the train is moving with constant velocity.
b) In front of the person if the train is accelerating.
c) Behind the person if the train is decelerating.
d) All of the above are correct.

The magnitude of displacement is always:

(a) Greater than the distance travelled.
b) Equal to the distance travelled.
c) Less than or equal to the distance travelled.
d) Less than the distance travelled.

A particle completes one full circle of radius R in time T. The distance travelled is ________ and the
displacement is ________.
a) 2πR; zero
b) zero; 2πR
c) 2πR; 2R
d) 2R; 2πR

The speedometer of a car measures its:

(a) Average speed (b) Instantaneous speed (c) Average velocity (d) Instantaneous velocity

A negative acceleration means:

(a) The body is speeding up in the negative direction.
b) The body is slowing down (retardation).
c) The velocity vector is changing direction.
d) Both a and b can be correct depending on the direction of initial velocity.

For projectile motion, the velocity and acceleration vectors are perpendicular to each other at:
(a) The point of projection (b) The point of landing (c) The highest point of the trajectory (d) Never

Two bodies are projected with the same speed, but at different angles (30° and 60°). The ratio of
their maximum heights will be:
(a) 1:3 (b) 3:1 (c) 1:√3 (d) √3:1

A stone tied to a string is whirled in a horizontal circle. If the string breaks, the stone will fly off:
(a) Radially outwards (b) Radially inwards (c) Tangentially to its circular path (d) In a random
direction

The statement "a body at rest will remain at rest, and a body in motion will remain in motion,
 unless acted upon by a net external force" is:
(a) Newton's First Law of Motion (b) Newton's Second Law of Motion (c) Newton's Third Law of
Motion (d) The Law of Conservation of Energy

Inertia is the property of a body by virtue of which it resists a change in its state of:
(a) Rest only (b) Uniform motion only (c) Rest or uniform motion (d) Acceleration

A passenger in a moving bus tends to fall forward when the bus suddenly stops. This is an
example of:
(a) Inertia of rest (b) Inertia of motion (c) Inertia of direction (d) Newton's third law

Section 4: Dynamics (Newton's Laws & Friction) (66-101)

1. Newton's Second Law of Motion gives a measure of force as the:
(a) Product of mass and velocity (momentum).
b) Rate of change of momentum (F = dp/dt).
c) Product of mass and acceleration (F=ma).
d) Both b and c are correct statements of the law.

The SI unit of force is the Newton (N), which is equivalent to:

(a) kg·m/s² (b) kg·m/s (c) kg·m²/s² (d) J/s

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.
The action and reaction forces:
(a) Act on the same body.
b) Act on two different bodies.
c) Cancel each other out.
d) Are not always equal.

The propulsion of a rocket is based on the principle of:

(a) Conservation of energy (b) Conservation of angular momentum (c) Conservation of linear
momentum (d) Newton's first law

A person is standing in an elevator that is accelerating upwards. The apparent weight of the
person will be:
(a) Greater than their true weight (mg).
b) Less than their true weight.
c) Equal to their true weight.
d) Zero.

The condition of weightlessness is experienced in a satellite or an elevator that is:

(a) Accelerating upwards (b) Accelerating downwards with a=g (freely falling) (c) Moving with
constant velocity (d) At rest

Impulse is defined as the product of force and the time interval for which it acts. It is equal to the:
(a) Change in momentum (b) Rate of change of momentum (c) Change in kinetic energy (d) Work
done

The force of friction is a self-adjusting, tangential force that always ________ the relative motion
between surfaces in contact.
(a) opposes (b) aids (c) is perpendicular to (d) is independent of

Static friction is the friction that acts when there is no relative motion. The maximum value of
static friction is called:
(a) Kinetic friction (b) Limiting friction (c) Rolling friction (d) Fluid friction

The coefficient of static friction (μs) is generally ________ the coefficient of kinetic friction (μk).
a) less than (b) equal to (c) greater than (d) the reciprocal of

The law of friction states that the force of friction is independent of the ________ and directly
proportional to the ________.
a) area of contact; normal reaction
b) normal reaction; area of contact
c) speed; normal reaction
d) area of contact; speed

It is easier to roll a barrel than to pull it. This is because:

(a) Rolling friction is less than sliding friction.
b) Sliding friction is less than rolling friction.
c) The normal reaction is less in rolling.
d) The area of contact is greater in rolling.

The angle of repose (θ) is the minimum angle of inclination of a plane with the horizontal such
that a body placed on it just begins to slide down. It is related to the coefficient of static friction
by:
(a) μs = sin(θ) (b) μs = cos(θ) (c) μs = tan(θ) (d) μs = cot(θ)

A cricketer lowers his hands while catching a ball to:

(a) Decrease the ball's momentum.
b) Increase the time of impact, thereby decreasing the force exerted on his hands.
c) Decrease the impulse.
d) Increase the change in kinetic energy.

A man of mass 60 kg is in a lift. The lift descends with an acceleration of 4.9 m/s². The apparent
weight of the man is: (g = 9.8 m/s²)
(a) 588 N (b) 294 N (c) 882 N (d) Zero

A block is pulled on a rough horizontal surface by a force F. The work done by friction is always:
(a) Positive (b) Negative (c) Zero (d) Dependent on the direction of F

The slope of a momentum (p) vs. time (t) graph gives the:
(a) Impulse (b) Acceleration (c) Force (d) Kinetic energy

A horse pulls a cart. The force that causes the horse-cart system to move forward is the:
(a) Force exerted by the horse on the cart.
b) Force exerted by the cart on the horse.
c) Force exerted by the horse on the ground.
d) Frictional force exerted by the ground on the horse.

The mass of a body is a measure of its:

(a) Weight (b) Inertia (c) Momentum (d) Force

A block of mass 'm' is at rest on an inclined plane with angle of inclination θ. The normal reaction
force is:
(a) mg (b) mg sin(θ) (c) mg cos(θ) (d) mg tan(θ)

A connected-body problem involves two masses m₁ and m₂ connected by a string over a pulley.
The tension in the string is:
(a) The same throughout if the string is massless and the pulley is frictionless.
b) Greater on the side of the heavier mass.
c) Greater on the side of the lighter mass.
d) Zero.

Banking of roads is done to:

(a) Increase the friction on the road.
b) Provide the necessary centripetal force from the normal reaction component.
c) Decrease the speed limit.
d) Increase the radius of the turn.

The maximum safe speed for a car to take a turn of radius 'r' on a banked road (angle θ) with
friction (μs) is given by a formula involving:
(a) Only r and θ (b) Only r and μs (c) r, θ, and μs (d) Only r

A system is in equilibrium if the:

(a) Net force on the system is zero.
b) Net torque on the system is zero.
c) System is not accelerating.
d) Both net force and net torque are zero.
The principle of conservation of linear momentum states that if the net external ________ on a
system is zero, its total ________ remains constant.
a) force; momentum
b) torque; angular momentum
c) force; kinetic energy
d) work; potential energy

The recoil of a gun after firing a bullet is an excellent example of:

(a) Newton's first law (b) Conservation of energy (c) Newton's second law (d) Conservation of
linear momentum

The force required to keep a body in uniform circular motion is the:

(a) Centrifugal force (b) Centripetal force (c) Frictional force (d) Gravitational force

The "centrifugal force" is considered a:

(a) Real force acting towards the center.
b) Real force acting away from the center.
c) Pseudo force that appears in a non-inertial (rotating) frame of reference.
d) Frictional force.

Which of the following is a self-adjusting force?

(a) Gravitational force (b) Tension (c) Normal reaction (d) Static friction

A body is moving on a circular path with constant speed. It has:

(a) Constant velocity.
b) Constant acceleration.
c) An acceleration of constant magnitude but changing direction.
d) No acceleration.

A bomb at rest explodes into two fragments of masses m₁ and m₂. The ratio of the magnitudes of
their momenta (p₁/p₂) is:
(a) m₁/m₂ (b) m₂/m₁ (c) 1:1 (d) √(m₁/m₂)

In the previous question, the ratio of their kinetic energies (KE₁/KE₂) is:
(a) m₁/m₂ (b) m₂/m₁ (c) 1:1 (d) √(m₁/m₂)

A ball is dropped from a height and it bounces back. The impulse on the ball during its collision
with the ground is:
(a) Zero (b) Directed upwards (c) Directed downwards (d) Dependent on the time of contact

Match the law (Column I) with its consequence (Column II):

| Column I | Column II |
|---|---|
| P. Newton's First Law | 1. Defines Force (F=ma) |
| Q. Newton's Second Law | 2. F_AB = -F_BA |
| R. Newton's Third Law | 3. Defines Momentum |
| S. Law of Conservation of Momentum | 4. Defines Inertia |
(a) P-1, Q-2, R-3, S-4
(b) P-4, Q-1, R-2, S-3 (derived from 2nd & 3rd)
(c) P-4, Q-3, R-2, S-1
(d) P-2, Q-1, R-4, S-3

Match the type of motion (Column I) with the correct description (Column II):
| Column I | Column II |
|---|---|
| P. Uniform Velocity | 1. Acceleration is constant (not zero) |
| Q. Uniform Acceleration | 2. Velocity is constant, Acceleration is zero |
| R. Projectile Motion | 3. Velocity is constant in one direction, acceleration in another |
| S. Uniform Circular Motion | 4. Speed is constant, velocity changes, acceleration towards center |
(a) P-1, Q-2, R-3, S-4
(b) P-2, Q-3, R-1, S-4
(c) P-2, Q-1, R-3, S-4
(d) P-4, Q-1, R-2, S-3

Match the type of friction (Column I) with its description (Column II):
 | Column I | Column II |
|---|---|
| P. Static Friction | 1. Friction on wheels |
| Q. Kinetic Friction | 2. Maximum static friction |
| R. Rolling Friction | 3. Friction when body is in motion |
| S. Limiting Friction | 4. Friction when body is at rest |
(a) P-1, Q-2, R-3, S-4
(b) P-4, Q-3, R-2, S-1
(c) P-4, Q-3, R-1, S-2
(d) P-2, Q-3, R-1, S-4

Section 5: Work, Energy, and Power (102-136)

1. Work is said to be done by a force when:
(a) The force is applied to a body.
(b) The body is displaced.
(c) The force causes a displacement of the body in the direction of the force.
(d) The body accelerates.

The SI unit of work is the ________, and its dimensional formula is ________.
a) Watt; [ML²T⁻³]
b) Joule; [ML²T⁻²]
c) Newton; [MLT⁻²]
d) Erg; [ML²T⁻²]

A man pushes against a rigid wall with a force of 100 N for 10 seconds but the wall does not
move. The work done by the man is:
(a) 1000 J (b) 10 J (c) 1 J (d) Zero

Work done by a variable force is calculated by:

(a) The product of the average force and displacement.
(b) The area under the Force-Displacement graph.
(c) The slope of the Force-Displacement graph.
(d) The product of the maximum force and displacement.

The work done by a centripetal force on a body in uniform circular motion is always:
(a) Positive (b) Negative (c) Zero (d) Infinite

Energy is defined as the:

(a) Rate of doing work. (b) Capacity to do work. (c) Change in momentum. (d) Product of force
and time.

The Work-Energy Theorem states that the net work done on a body is equal to the change in its:
(a) Potential energy (b) Kinetic energy (c) Momentum (d) Total energy

The kinetic energy of a body of mass 'm' moving with velocity 'v' is given by K = ½mv². If the
velocity is doubled, the kinetic energy becomes:
(a) Halved (b) Doubled (c) Four times (d) Unchanged

The potential energy stored in a spring with spring constant 'k' when it is stretched by a distance
'x' is:
(a) kx (b) ½kx (c) kx² (d) ½kx²

The Law of Conservation of Energy states that:

(a) Energy can be created but not destroyed.
b) The total energy of an isolated system remains constant.
c) Kinetic energy is always conserved.
d) Potential energy is always conserved.

A force is said to be conservative if the work done by the force:

(a) Is path-dependent. (b) Is path-independent and depends only on initial and final positions. (c)
Is always zero. (d) Is always positive.
Which of the following is a non-conservative force?
(a) Gravitational force (b) Electrostatic force (c) Elastic spring force (d) Frictional force

Power is defined as the:

(a) Total work done. (b) Total energy possessed by a body. (c) Rate at which work is done or
energy is transferred. (d) Product of force and displacement.

The SI unit of power is the Watt (W), which is equivalent to:

(a) Joule . second (J·s) (b) Joule / second (J/s) (c) Newton . meter (N·m) (d) kg·m/s

One horsepower (hp) is approximately equal to:

(a) 1000 W (b) 746 W (c) 550 W (d) 1 W

The relationship between power (P), force (F), and velocity (v) is:
(a) P = F / v (b) P = F . v (c) P = F x v (d) P = Fv²

In an inelastic collision, which of the following is conserved?

(a) Only kinetic energy (b) Only momentum (c) Both momentum and kinetic energy (d) Neither
momentum nor kinetic energy

In a perfectly elastic collision, which of the following is conserved?

(a) Only kinetic energy (b) Only momentum (c) Both momentum and kinetic energy (d) Only
potential energy

The coefficient of restitution (e) is a measure of the elasticity of a collision. For a perfectly elastic
collision, e = ________, and for a perfectly inelastic collision, e = ________.
a) 1; 0 (b) 0; 1 (c) infinity; 0 (d) 1; infinity

A body of mass 2 kg and another body of mass 4 kg have the same momentum. The ratio of their
kinetic energies is:
(a) 2:1 (b) 1:2 (c) 4:1 (d) 1:4

A light body and a heavy body have the same kinetic energy. Which one has greater momentum?
(a) The light body (b) The heavy body (c) Both have the same momentum (d) Cannot be
determined

The relationship between kinetic energy (K) and linear momentum (p) is:
(a) K = p²/2m (b) K = 2m/p² (c) K = p/2m (d) K = 2mp

A coolie lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground.
The work done by him on the luggage is: (g = 10 m/s²)
(a) 150 J (b) 225 J (c) 1.5 J (d) Zero

A ball is dropped from a height 'h'. Just before hitting the ground, its energy is:
(a) Purely potential (b) Purely kinetic (c) Partly potential and partly kinetic (d) Zero

Power can also be defined as the scalar product of:

(a) Force and acceleration (b) Force and displacement (c) Force and velocity (d) Force and
momentum

If the kinetic energy of a body increases by 300%, its momentum will increase by:
(a) 50% (b) 100% (c) 150% (d) 200%

The potential energy of a system increases if work is done:

(a) By the system against a conservative force.
b) On the system by a conservative force.
c) By the system against a non-conservative force.
d) On the system by a non-conservative force.

A spring is stretched by a distance x. The potential energy stored is U. If it is stretched by a

distance 2x, the potential energy stored will be:
(a) U/2 (b) 2U (c) 4U (d) U/4

Work done can be:

 (a) Positive only (b) Negative only (c) Zero only (d) Positive, negative, or zero

In which of the following cases is the work done negative?

(a) Work done by the force of gravity on a freely falling body.
b) Work done by the force of friction on a moving body.
c) Work done by an applied force to lift a body.
d) Work done in stretching a spring.

The area enclosed by the Force-Displacement graph for a conservative force in a closed loop is:
(a) Positive (b) Negative (c) Zero (d) Equal to the change in KE

One electron-volt (eV) is a unit of:

(a) Potential (b) Charge (c) Power (d) Energy

Two particles of masses m₁ and m₂ have equal kinetic energies. The ratio of their linear momenta
is:
(a) m₁:m₂ (b) m₂:m₁ (c) √(m₁):√(m₂) (d) √(m₂):√(m₁)

In a one-dimensional elastic collision of two identical bodies, one of which is at rest:

(a) They stick together after the collision.
b) They exchange their velocities.
c) The moving body comes to rest and the other moves with half the velocity.
d) Both bodies move together with half the initial velocity.

A bomb at rest explodes into many pieces. The kinetic energy of the system ________, and the
momentum of the system ________.
a) increases; is conserved (remains zero)
b) is conserved; increases
c) increases; increases
d) is conserved; is conserved

Section 6: Circular Motion (137-166)

1. The physical quantity that is analogous to linear displacement in rotational motion is:
(a) Angular velocity (b) Angular acceleration (c) Angular displacement (d) Torque

The SI unit of angular velocity is:

(a) revolution/second (b) degree/second (c) radian/second (rad/s) (d) meter/second

The relationship between linear velocity (v), angular velocity (ω), and radius (r) is:
(a) v = ωr (b) ω = vr (c) r = vω (d) v = ω/r

A body is moving in a circle with constant speed. It has:

(a) Constant velocity. (b) Constant acceleration. (c) An acceleration of constant magnitude
directed towards the center. (d) No acceleration.

The force required to keep an object moving in a circular path is the:

(a) Centrifugal force (b) Centripetal force (c) Frictional force (d) Gravitational force

The expression for centripetal force (F_c) is:

(a) mv²/r (b) mω²r (c) mvω (d) All of the above

A cyclist leans inwards while taking a turn on a level road to:

(a) Reduce friction. (b) Decrease their speed. (c) Provide the necessary centripetal force from the
component of the normal reaction. (d) Increase the radius of the turn.

The "centrifugal force" is considered a:

(a) Real force acting towards the center. (b) Real force acting away from the center. (c) Fictitious
or pseudo force that appears in a non-inertial (rotating) frame of reference. (d) Frictional force.

For a car to safely navigate a banked curve of radius r and angle θ without relying on friction, the
required speed is:
(a) √(rg sinθ) (b) √(rg cosθ) (c) √(rg tanθ) (d) √(rg/tanθ)
A bucket of water is whirled in a vertical circle. The water does not fall out at the top of the circle
if the speed is such that the:
(a) Centripetal force is zero. (b) Weight of the water is greater than the required centripetal force.
(c) Weight of the water is less than or equal to the required centripetal force. (d) Centrifugal force
is zero.

The minimum speed required at the top of a vertical circle of radius 'r' to complete the loop is:
(a) √(2gr) (b) √(3gr) (c) √(5gr) (d) √(gr)

The minimum speed required at the bottom of a vertical circle of radius 'r' to complete the loop is:
(a) √(2gr) (b) √(3gr) (c) √(5gr) (d) √(gr)

The relationship between angular acceleration (α) and tangential acceleration (a_t) is:
(a) a_t = αr (b) α = a_t r (c) a_t = α/r (d) r = a_t α

A fan rotating at 120 rpm has an angular velocity of:

(a) 2π rad/s (b) 4π rad/s (c) 120 rad/s (d) 2 rad/s

If a particle in circular motion speeds up, its total acceleration is the vector sum of the:
(a) Centripetal and centrifugal accelerations. (b) Centripetal and tangential accelerations. (c)
Tangential and angular accelerations. (d) Linear and angular accelerations.

In non-uniform circular motion:

(a) The speed is constant. (b) The tangential acceleration is zero. (c) The angular velocity is
constant. (d) The speed and angular velocity are changing.

A cream separator works on the principle of:

(a) Centripetal force (b) Centrifugal force (c) Gravitational force (d) Frictional force

A car is moving on a circular level road of radius R with a speed V. The coefficient of friction
between the tyres and the road is μ. The car will skid if:
(a) V² > μRg (b) V² < μRg (c) V² = μRg (d) V > μg

The tension in the string at the lowest point of a vertical circle is ________ the tension at the
highest point.
a) equal to
b) less than
c) greater than
d) sometimes greater, sometimes less than

The work done by the centripetal force in one complete revolution is:
(a) mv²/r × 2πr (b) Zero (c) 2πmv² (d) πr²F_c

The time period (T) and frequency (f) of a particle in uniform circular motion are related by:
(a) T = f (b) T = f² (c) T = 1/f (d) T = 2πf

A satellite orbiting the Earth is an example of:

(a) Uniform circular motion (approximately). (b) Projectile motion. (c) Simple harmonic motion.
(d) Linear motion.

When a particle moves in a circle, the angle between its velocity vector and acceleration vector is:
(a) Always 0° (b) Always 90° for uniform circular motion (c) Always 180° (d) Varies from 0° to
180°

An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 45°. The
radius of the loop is: (g = 10 m/s²)
(a) 1 km (b) 2 km (c) 4 km (d) 8 km

In a conical pendulum, the centripetal force is provided by the:

(a) Vertical component of the tension. (b) Horizontal component of the tension. (c) Weight of the
bob. (d) Entire tension in the string.

The equations of rotational motion are analogous to the equations of linear motion, with ________
replacing ________.
 a) θ, ω, α; s, v, a
b) s, v, a; θ, ω, α
c) Torque, Force; Mass
d) Mass; Moment of Inertia

A body is released from a height 'h' on a smooth inclined plane so that it completes a vertical
circle of radius 'R' at the bottom. The minimum value of 'h' is:
(a) 2R (b) 5R (c) 5R/2 (d) 3R/2

The angular speed of the minute hand of a clock is:

(a) π/1800 rad/s (b) π/30 rad/s (c) π/60 rad/s (d) 2π rad/s

The centripetal acceleration of a particle moving in a circle of radius 2 m at a speed of 4 m/s is:
(a) 2 m/s² (b) 4 m/s² (c) 8 m/s² (d) 16 m/s²

Match the term (Column I) with its description (Column II):

| Column I | Column II |
|---|---|
| P. Angular Velocity | 1. Change in angular velocity per unit time |
| Q. Angular Acceleration | 2. Rate of change of angular displacement |
| R. Centripetal Force | 3. Fictitious force in a rotating frame |
| S. Centrifugal Force | 4. Force required for circular motion |
(a) P-1, Q-2, R-3, S-4
(b) P-2, Q-1, R-4, S-3
(c) P-2, Q-3, R-1, S-4
(d) P-4, Q-1, R-2, S-3

Section 7: Gravitation (167-201)

1. Newton's Law of Universal Gravitation states that the force of attraction between any two bodies
is:
(a) Directly proportional to the product of their masses and inversely proportional to the distance
between them.
b) Directly proportional to the product of their masses and inversely proportional to the square of
the distance between them.
c) Inversely proportional to the product of their masses.
d) Independent of the distance between them.

The value of the universal gravitational constant (G) is:

(a) 9.8 m/s² (b) 6.67 x 10⁻¹¹ N·m²/kg² (c) 6.022 x 10²³ (d) 8.99 x 10⁹ N·m²/C²

The acceleration due to gravity (g) at the surface of the Earth is given by: (M=mass of Earth,
R=radius of Earth)
(a) g = GM/R (b) g = GM/R² (c) g = G/R² (d) g = GR²/M

As one goes from the equator to the poles, the value of 'g':
(a) Decreases (b) Increases (c) Remains constant (d) First decreases then increases

The value of 'g' at a height 'h' above the Earth's surface (for h << R) is approximately:
(a) g(1 - h/R) (b) g(1 - 2h/R) (c) g(1 + 2h/R) (d) gR²/(R+h)²

The value of 'g' at a depth 'd' below the Earth's surface is given by:
(a) g(1 - d/R) (b) g(1 - 2d/R) (c) g(1 + d/R) (d) gR/(R-d)

At the center of the Earth, the value of 'g' is:

(a) Maximum (b) The same as on the surface (c) Half of the value on the surface (d) Zero

The minimum velocity required for an object to escape the Earth's gravitational field is the escape
velocity. Its value is approximately:
(a) 7.9 km/s (b) 9.8 km/s (c) 11.2 km/s (d) 22.4 km/s

The escape velocity (v_e) from the surface of a planet is related to the orbital velocity (v_o) of a
satellite orbiting close to the surface by:
(a) v_e = v_o (b) v_e = 2v_o (c) v_e = √2 v_o (d) v_o = √2 v_e

The orbital velocity of a satellite orbiting the Earth at a height 'h' depends on:
(a) The mass of the satellite. (b) The mass and radius of the Earth. (c) The height of the satellite.
(d) Both b and c.

A geostationary satellite is one which:

(a) Orbits the Earth from pole to pole.
b) Appears stationary with respect to a point on the Earth's surface.
c) Has a time period of 24 hours.
d) Both b and c are correct.

The weight of a body is the force with which the Earth attracts it. It is maximum at the ________
and minimum at the ________.
a) poles; equator
b) equator; poles
c) center of the Earth; surface
d) surface; center of the Earth

Kepler's first law of planetary motion states that planets revolve around the Sun in:
(a) Circular orbits with the Sun at the center.
b) Elliptical orbits with the Sun at one of the foci.
c) Parabolic paths.
d) Hyperbolic paths.

Kepler's second law (law of areas) is a consequence of the conservation of:

(a) Linear momentum (b) Energy (c) Angular momentum (d) Mass

Kepler's third law of planetary motion relates the time period (T) and the semi-major axis (a) of
the orbit as:
(a) T² a³ (b) T a² (c) T³ a² (d) T a

Gravitational potential at a point is the work done in bringing a unit mass from infinity to that
point. It is always:
(a) Positive (b) Negative (c) Zero (d) Infinite

The intensity of the gravitational field is zero:

(a) At the surface of the Earth (b) At the equator (c) At the poles (d) At the center of the Earth

If the radius of the Earth were to shrink by 1% while its mass remains the same, the acceleration
due to gravity on the surface would:
(a) Decrease by 1% (b) Decrease by 2% (c) Increase by 1% (d) Increase by 2%

A satellite is orbiting the Earth. If its speed is increased, it will:

(a) Fall back to Earth. (b) Move into a higher orbit. (c) Move into a lower orbit. (d) Continue in the
same orbit.

The time period of a simple pendulum in a satellite orbiting the Earth is:
(a) Zero (b) Infinite (c) 2π√(L/g) (d) Dependent on the satellite's speed

The binding energy of a satellite of mass 'm' orbiting the Earth is the energy required to remove it
from its orbit to infinity. It is equal to:
(a) -GMm/2r (b) +GMm/2r (c) -GMm/r (d) +GMm/r

Which of the following statements is true for a satellite orbiting the Earth?
(a) Its kinetic energy is constant. (b) Its potential energy is constant. (c) Its total energy is
constant. (d) Its linear momentum is constant.

The tides in the sea are primarily due to the:

(a) Gravitational effect of the Sun on the Earth.
b) Gravitational effect of the Moon on the Earth.
c) Rotation of the Earth.
d) Gravitational effect of Venus.
 The gravitational force is a:
(a) Short-range force (b) Strong nuclear force (c) Weak nuclear force (d) Long-range, conservative
force

The escape velocity from the Earth's surface is independent of the:

(a) Mass of the Earth (b) Radius of the Earth (c) Mass of the body being launched (d)
Gravitational constant

Two spheres of masses m and M are situated in air and the gravitational force between them is F.
If the space around the masses is filled with a liquid of specific gravity 3, the gravitational force
will be:
(a) F (b) 3F (c) F/3 (d) 9F

The value of 'g' at the poles is greater than at the equator due to the:
(a) Rotation of the Earth (centrifugal effect).
b) Earth being slightly flattened at the poles and bulging at the equator.
c) Presence of ice at the poles.
d) Both a and b.

The total energy of a satellite in a circular orbit is:

(a) Positive (b) Negative (c) Zero (d) Equal to its kinetic energy

Match the law/principle (Column I) with the conserved quantity (Column II):
| Column I | Column II |
|---|---|
| P. Law of Areas (Kepler's 2nd) | 1. Total Energy |
| Q. Newton's Law of Gravitation | 2. Angular Momentum |
| R. Conservative Force Field | 3. Linear Momentum |
| S. Absence of Net External Force | 4. Acts on mass |
(a) P-1, Q-2, R-3, S-4
(b) P-2, Q-4, R-1, S-3
(c) P-2, Q-3, R-1, S-4
(d) P-4, Q-1, R-2, S-3

Section 8: Elasticity (196-201)

1. Elasticity is the property of a body by virtue of which it:
(a) Resists a change in its shape or size.
b) Regains its original shape and size after the removal of a deforming force.
c) Remains in the deformed state.
d) Breaks when a force is applied.

Stress is defined as the ________, and its SI unit is ________.

a) change in dimension per unit original dimension; dimensionless
b) restoring force per unit area; N/m² or Pascal
c) total deforming force; Newton
d) work done in deforming; Joule

Strain is defined as the:

(a) Restoring force per unit area.
b) Total deforming force.
c) Change in dimension divided by the original dimension.
d) Energy stored per unit volume.

Hooke's Law states that within the elastic limit:

(a) Stress is equal to strain. (b) Stress is inversely proportional to strain. (c) Stress is directly
proportional to strain. (d) Strain is constant.

The modulus of elasticity (Young's modulus, Bulk modulus, or Shear modulus) is the ratio of:
(a) Strain to Stress (b) Stress to Strain (c) Force to Area (d) Change in length to original length

Which of the following is the most elastic material?

(a) Rubber (b) Clay (c) Steel (d) Plastic
Section 1: Rotational Dynamics (202-236)
1. The physical quantity in rotational motion that is analogous to mass in linear motion is the:
(a) Torque (b) Angular momentum (c) Moment of inertia (d) Angular velocity

The moment of inertia of a body does NOT depend on its:

(a) Mass (b) Distribution of mass (c) Axis of rotation (d) Angular velocity

The rotational equivalent of Newton's second law of motion (F=ma) is:

(a) τ = Iα (b) L = Iω (c) P = τω (d) K = ½Iω²

The turning effect of a force about an axis of rotation is called:

(a) Impulse (b) Power (c) Torque (d) Momentum

Torque (τ) is a vector quantity defined as the cross product of the position vector (r) and the
force (F). Its formula is:
(a) τ = r . F (b) τ = r x F (c) τ = F x r (d) τ = F . r

The moment of inertia of a thin circular ring of mass M and radius R about an axis passing
through its center and perpendicular to its plane is:
(a) MR² (b) ½MR² (c) MR²(d) MR²

The moment of inertia of a uniform circular disc of mass M and radius R about an axis passing
through its center and perpendicular to its plane is:
(a) MR² (b) ½MR² (c) MR²(d) MR²

The Theorem of Parallel Axes states that the moment of inertia (I) about any axis is related to
the moment of inertia about a parallel axis through the center of mass (I_cm) by: (M=mass,
d=distance between axes)
(a) I = I_cm + Md² (b) I = I_cm - Md² (c) I_cm = I + Md² (d) I = I_cm

The Theorem of Perpendicular Axes is applicable only to:

(a) Three-dimensional bodies (b) Spherical bodies (c) All bodies (d) Planar bodies (laminas)

The radius of gyration (K) of a body is the distance from the axis of rotation where the entire
mass could be concentrated to give the same moment of inertia. It is related to moment of
inertia (I) by:
(a) I = M/K² (b) I = MK² (c) I = M²K (d) I = K/M²

The angular momentum (L) of a rigid body is the product of its moment of inertia (I) and its
angular velocity (ω). It is given by:
(a) L = I/ω (b) L = ω/I (c) L = Iω (d) L = Iω²

The law of conservation of angular momentum states that if the net external ________ on a
system is zero, its ________ remains constant.
a) force; linear momentum
b) torque; angular momentum
c) force; angular momentum
d) torque; linear momentum

A ballet dancer spinning on ice can increase her angular speed by pulling her arms in. This is an
application of:
(a) Conservation of energy (b) Conservation of linear momentum (c) Conservation of angular
momentum (d) Newton's third law

A solid sphere and a hollow sphere of the same mass and radius are allowed to roll down an
inclined plane from the same height. Which one will reach the bottom first?
(a) The solid sphere (b) The hollow sphere (c) Both will reach simultaneously (d) Depends on
the angle of inclination

The rotational kinetic energy of a body is given by:

(a) ½mv² (b) Iω (c) ½Iω² (d) τω

For a body rolling without slipping, the total kinetic energy is the sum of its:
(a) Rotational and potential energies.
b) Translational and rotational kinetic energies.
c) Only rotational kinetic energy.
d) Only translational kinetic energy.

The SI unit of torque is ________, and the SI unit of angular momentum is ________.
a) N·m; kg·m²/s
b) N/m; kg·m/s
c) J/s; kg·m²/s²
d) N·m; J·s

The moment of inertia of a uniform rod of mass M and length L about an axis through its
center and perpendicular to its length is:
(a) ML²/3 (b) ML²/12 (c) ML² (d) ½ML²

The moment of inertia of a solid sphere of mass M and radius R about its diameter is:
(a) MR² (b) ½MR² (c) MR²(d) MR²

An object is in rotational equilibrium if:

(a) The net force acting on it is zero.
b) It is not moving.
c) The net external torque acting on it is zero.
d) Its angular velocity is constant.

The power delivered by a torque (τ) rotating a body with angular velocity (ω) is:
(a) P = τ/ω (b) P = τω (c) P = τ x ω (d) P = τ . ω

When a disc rotates, which part moves the fastest?

(a) The center (b) The rim (c) The midpoint of the radius (d) All parts move at the same linear
speed.

If a body's angular velocity is constant, its angular acceleration is:

(a) Constant and non-zero (b) Zero (c) Variable (d) Infinite

A couple is a pair of forces that are:

(a) Equal and acting in the same direction.
b) Equal and opposite, but acting along the same line.
c) Unequal and opposite.
d) Equal, opposite, and separated by a distance, producing only rotation.

The center of mass of a system is a point where:

(a) All the mass is physically concentrated.
b) The gravitational force is zero.
c) The entire mass of the system is assumed to be concentrated for describing its translational
motion.
d) The moment of inertia is always zero.

For a uniform triangular lamina, the center of mass is at its:

(a) Vertex (b) Midpoint of the base (c) Centroid (d) Incenter

Two particles of masses 1 kg and 3 kg are separated by a distance of 4 m. The center of mass
is located at a distance of ________ from the 1 kg mass.
(a) 1 m (b) 2 m (c) 3 m (d) 4 m

The motion of the center of mass of a system is affected only by:

(a) Internal forces (b) External forces (c) Both internal and external forces (d) Conservative
forces

A flywheel is used in an engine to:

(a) Increase its power. (b) Decrease friction. (c) Store rotational kinetic energy and maintain a
uniform speed. (d) Increase its speed.
 The rotational analogue of impulse is:
(a) Torque (b) Angular impulse (τΔt) (c) Angular momentum (d) Moment of inertia

If the Earth were to suddenly shrink to half its present radius (mass remaining constant), the
length of the day would be:
(a) 24 hours (b) 12 hours (c) 6 hours (d) 48 hours

The moment of inertia of a hollow cylinder is ________ that of a solid cylinder of the same mass
and radius.
(a) less than (b) equal to (c) greater than (d) half

The condition for a body to roll without slipping on a surface is:

(a) v_cm = Rω (b) v_cm > Rω (c) v_cm < Rω (d) v_cm = 0

The direction of angular momentum is given by the:

(a) Left-hand rule (b) Right-hand grip rule (c) Fleming's rule (d) Lenz's law

Match the linear quantity (Column I) with its rotational analogue (Column II):
| Column I | Column II |
|---|---|
| P. Mass (m) | 1. Torque (τ) |
| Q. Force (F) | 2. Angular Momentum (L) |
| R. Linear Momentum (p) | 3. Angular Velocity (ω) |
| S. Linear Velocity (v) | 4. Moment of Inertia (I) |
(a) P-1, Q-2, R-3, S-4
(b) P-4, Q-1, R-2, S-3
(c) P-4, Q-2, R-1, S-3
(d) P-2, Q-1, R-4, S-3

Section 2: Periodic Motion (SHM) (237-266)

1. A motion that repeats itself over a regular interval of time is called:
(a) Simple harmonic motion (b) Oscillatory motion (c) Periodic motion (d) Translational motion

Simple Harmonic Motion (SHM) is a special type of periodic motion where the restoring force
is directly proportional to the ________ and is directed ________ the equilibrium position.
a) displacement; away from
b) displacement; towards
c) velocity; towards
d) velocity; away from

The equation for a particle in SHM is given by y = A sin(ωt + φ). The term 'A' represents the:
(a) Frequency (b) Time period (c) Amplitude (d) Phase constant

The time taken for a particle in SHM to complete one full oscillation is its:
(a) Frequency (b) Period (T) (c) Angular frequency (ω) (d) Amplitude

The relationship between angular frequency (ω), frequency (f), and period (T) is:
(a) ω = 2πf = 2π/T (b) f = 2πω = 2π/T (c) T = 2πf = 2π/ω (d) ω = f/2π

In SHM, the velocity of the particle is maximum at the ________ and zero at the ________.
a) mean position; extreme positions
b) extreme positions; mean position
c) It is constant throughout.
d) It is zero everywhere.

In SHM, the acceleration of the particle is maximum at the ________ and zero at the ________.
a) mean position; extreme positions
b) extreme positions; mean position
c) It is constant throughout.
d) It is zero everywhere.

The phase difference between the displacement and velocity of a particle in SHM is:
(a) 0 (b) π/2 (90°) (c) π (180°) (d) 3π/2

The phase difference between the displacement and acceleration of a particle in SHM is:
(a) 0 (b) π/2 (c) π (180°) (d) 3π/2

The time period of a simple pendulum of length 'L' is given by T = 2π√(L/g). It is independent of
the:
(a) Length of the pendulum (L) (b) Acceleration due to gravity (g) (c) Mass and amplitude of the
bob (for small oscillations) (d) Both a and b

A "seconds pendulum" is a simple pendulum whose time period is:

(a) 1 second (b) 2 seconds (c) 0.5 seconds (d) 9.8 seconds

The time period of a mass 'm' attached to a spring with spring constant 'k' is given by:
(a) T = 2π√(m/k) (b) T = 2π√(k/m) (c) T = 2π√(L/g) (d) T = 2π√(g/L)

If the length of a simple pendulum is quadrupled, its new time period will be:
(a) Halved (b) Doubled (c) Four times (d) Unchanged

The total energy of a particle executing SHM is:

(a) Always kinetic (b) Always potential (c) Constant at all points (d) Maximum at the mean
position

A damped oscillation is one where the:

(a) Amplitude remains constant over time.
b) Amplitude decreases exponentially over time due to resistive forces.
c) Frequency changes over time.
d) Oscillation is driven by an external force.

Resonance occurs when the frequency of an external driving force is:

(a) Much greater than the natural frequency of the oscillator.
b) Much less than the natural frequency of the oscillator.
c) Equal to the natural frequency of the oscillator, leading to a large amplitude.
d) Zero.

The potential energy of a particle in SHM is maximum at the:

(a) Mean position (b) Extreme positions (c) A point midway between mean and extreme (d) It is
constant.

Which of the following is NOT an example of simple harmonic motion?

(a) The oscillation of a mass on a spring (ideal).
b) The swing of a simple pendulum (small amplitude).
c) The motion of a planet around the Sun.
d) The vibration of a tuning fork.

A particle in SHM has a period of 4 s. Its frequency is:

(a) 4 Hz (b) 2 Hz (c) 0.5 Hz (d) 0.25 Hz

For a body executing SHM, the force is given by F = -ky. The potential energy is:
(a) -ky² (b) ½ky² (c) ky (d) ½ky

If a simple pendulum is taken to the Moon, where gravity is 1/6th that of Earth, its time period
will:
(a) Decrease by a factor of 6 (b) Decrease by a factor of √6 (c) Increase by a factor of 6 (d)
Increase by a factor of √6

Lissajous figures are produced by the superposition of:

(a) Two sound waves.
b) Two light waves.
c) Two simple harmonic motions at right angles to each other.
d) Two damped oscillations.

In the equation y = A sin(ωt), 'y' represents the:

(a) Amplitude (b) Instantaneous displacement from the mean position (c) Time period (d)
 Frequency

A spring has a spring constant k. If it is cut into two equal halves, the spring constant of each
half will be:
(a) k/2 (b) k (c) 2k (d) 4k

The restoring force in a simple pendulum is provided by the:

(a) Tension in the string. (b) Weight of the bob (mg). (c) Tangential component of the weight
(mg sinθ). (d) Centripetal force.

If two springs of spring constants k₁ and k₂ are connected in series, the equivalent spring
constant is:
(a) k₁ + k₂ (b) (k₁ + k₂)/2 (c) k₁k₂/(k₁ + k₂) (d) √(k₁k₂)

If the two springs from the previous question are connected in parallel, the equivalent spring
constant is:
(a) k₁ + k₂ (b) (k₁ + k₂)/2 (c) k₁k₂/(k₁ + k₂) (d) √(k₁k₂)

An example of a forced oscillation is:

(a) A tuning fork struck and left to vibrate.
b) A child on a swing being pushed periodically.
c) A simple pendulum swinging freely.
d) A guitar string plucked once.

The energy of an oscillator is proportional to the:

(a) Amplitude (b) Square of the amplitude (c) Frequency (d) Square root of the amplitude

A body is moving in a circular path with uniform speed. Its motion is:
(a) Periodic but not SHM (b) SHM but not periodic (c) Both periodic and SHM (d) Neither
periodic nor SHM

Section 3: Fluid Statics & Elasticity (267-301)

1. The study of fluids at rest is called:
(a) Fluid dynamics (b) Hydrostatics (or Fluid Statics) (c) Viscosity (d) Surface tension

Pressure in a fluid is defined as the:

(a) Total force acting on a surface. (b) Normal force per unit area. (c) Tangential force per unit
area. (d) Work done per unit volume.

Pascal's Law states that a pressure change at any point in a confined incompressible fluid is:
(a) Transmitted only downwards.
b) Transmitted undiminished to all points throughout the fluid.
c) Absorbed by the fluid.
d) Strongest at the point of application.

Hydraulic lifts and hydraulic brakes work on the principle of:

(a) Archimedes' Principle (b) Bernoulli's Principle (c) Pascal's Law (d) Torricelli's Law

The pressure at a depth 'h' inside a liquid of density 'ρ' is given by:
(a) P = ρgh (b) P = ρg/h (c) P = hg/ρ (d) P = ρh/g

Archimedes' Principle states that a body immersed in a fluid experiences an upward buoyant
force equal to the:
(a) Weight of the body. (b) Volume of the body. (c) Weight of the fluid displaced by the body. (d)
Mass of the fluid displaced.

A body floats in a liquid if the buoyant force is ________ the weight of the body.
(a) less than (b) equal to (c) greater than (d) the square root of

The fraction of a floating object of density ρ_obj that is submerged in a fluid of density ρ_fluid
is:
(a) ρ_fluid / ρ_obj (b) ρ_obj / ρ_fluid (c) (ρ_fluid - ρ_obj) / ρ_fluid (d) (ρ_obj - ρ_fluid) / ρ_obj
An iceberg floats in seawater with most of its volume submerged because:
(a) Ice is denser than seawater. (b) Ice is less dense than seawater. (c) Ice is hydrophilic. (d)
The pressure at the bottom is very high.

A hydrometer is an instrument used to measure the:

(a) Humidity of air (b) Pressure of a fluid (c) Velocity of a fluid (d) Specific gravity or relative
density of a liquid.

The pressure measured by a barometer is the:

(a) Gauge pressure (b) Absolute pressure (c) Atmospheric pressure (d) Vapor pressure

The property of a fluid that opposes the relative motion between its layers is:
(a) Surface tension (b) Buoyancy (c) Compressibility (d) Viscosity

According to Stokes' Law, the viscous drag force on a small sphere moving through a fluid is
proportional to its:
(a) Radius and velocity (b) Radius and velocity squared (c) Area and velocity (d) Radius
squared and velocity

The constant velocity attained by a body falling through a viscous fluid is called its:
(a) Escape velocity (b) Orbital velocity (c) Critical velocity (d) Terminal velocity

The equation of continuity for an ideal fluid in streamline flow (A₁v₁ = A₂v₂) is a statement of
the conservation of:
(a) Energy (b) Momentum (c) Mass (d) Charge

Bernoulli's principle relates the pressure, velocity, and height of a moving fluid and is a
statement of the conservation of:
(a) Mass (b) Momentum (c) Energy (d) Volume

The lifting of an aeroplane's wing (aerofoil) is an application of:

(a) Pascal's Law (b) Archimedes' Principle (c) Bernoulli's Principle (d) Stokes' Law

The flow of a fluid is said to be streamline if every particle of the fluid follows the exact path of
the preceding particle. Above a certain critical velocity, the flow becomes:
(a) Laminar (b) Turbulent (c) Steady (d) Uniform

The property of a body to regain its original shape and size after the removal of a deforming
force is:
(a) Plasticity (b) Elasticity (c) Ductility (d) Malleability

Stress is defined as ________, and its SI unit is ________.

a) change in dimension per original dimension; dimensionless
b) restoring force per unit area; N/m² (Pascal)
c) total deforming force; Newton
d) work done in deforming; Joule

Strain is defined as the:

(a) Restoring force per unit area.
b) Total deforming force.
c) Fractional change in dimension (ΔL/L, ΔV/V, etc.).
d) Energy stored per unit volume.

Hooke's Law states that within the elastic limit, stress is directly proportional to:
(a) Force (b) Strain (c) Temperature (d) Area

Young's Modulus of Elasticity (Y) is the ratio of:

(a) Bulk stress to bulk strain (b) Shear stress to shear strain (c) Longitudinal stress to
longitudinal strain (d) Force to extension

The Bulk Modulus (B) is a measure of a substance's resistance to:

(a) Change in length (b) Change in shape (c) Change in volume (d) Twisting

The reciprocal of the Bulk Modulus is the:

 (a) Compressibility (b) Young's Modulus (c) Rigidity Modulus (d) Poisson's Ratio

A substance that can be drawn into thin wires is ________, while one that can be hammered into
thin sheets is ________.
a) ductile; malleable
b) malleable; ductile
c) brittle; elastic
d) elastic; brittle

The energy stored per unit volume in a stretched wire is given by:
(a) Stress × Strain (b) ½ × Stress × Strain (c) Young's Modulus × Strain (d) Stress / Strain

Poisson's ratio is the ratio of:

(a) Longitudinal strain to lateral strain (b) Lateral strain to longitudinal strain (c) Shear stress to
shear strain (d) Stress to strain

For most materials, the theoretical value of Poisson's ratio lies between:
(a) 0 and 0.5 (b) -1 and 0.5 (c) 0.5 and 1 (d) -1 and 0

Which of the following is the most elastic?

(a) Rubber (b) Clay (c) Steel (d) Plastic

The breaking stress for a wire of a given material is:

(a) Dependent on its length. (b) Dependent on its thickness. (c) A constant for that material. (d)
Dependent on the temperature.

The property of a body to not regain its original shape at all after the removal of the deforming
force is called:
(a) Elasticity (b) Plasticity (c) Ductility (d) Brittleness

Match the term (Column I) with its description (Column II):

| Column I | Column II |
|---|---|
| P. Bernoulli's Principle | 1. Floating of ships |
| Q. Pascal's Law | 2. Motion of a pendulum |
| R. Archimedes' Principle | 3. Hydraulic brakes |
| S. Simple Harmonic Motion | 4. Lift of an aeroplane wing |
(a) P-1, Q-2, R-3, S-4
(b) P-4, Q-3, R-1, S-2
(c) P-4, Q-2, R-1, S-3
(d) P-2, Q-3, R-4, S-1

Match the modulus of elasticity (Column I) with the type of deformation (Column II):
| Column I | Column II |
|---|---|
| P. Young's Modulus (Y) | 1. Change in Volume |
| Q. Shear Modulus (G) | 2. Change in Shape |
| R. Bulk Modulus (B) | 3. Change in Length |
| S. Compressibility (k) | 4. Reciprocal of Bulk Modulus |
(a) P-1, Q-2, R-3, S-4
(b) P-3, Q-2, R-4, S-1
(c) P-3, Q-2, R-1, S-4
(d) P-2, Q-3, R-1, S-4

A body is considered to be perfectly rigid if its:

(a) Young's modulus is zero. (b) Bulk modulus is zero. (c) Shear modulus is zero. (d) All moduli
of elasticity are infinite.

Section 1: Advanced Kinematics & Vectors

1. A particle's position is given by r = (3t² i - 4t j + 5 k) m. The magnitude of its acceleration at t = 2

s is:
(a) 0 m/s² (b) 6 m/s² (c) 8 m/s² (d) 10 m/s²
 A river is flowing from west to east at a speed of 5 m/min. A man on the south bank of the river,
capable of swimming at 10 m/min in still water, wants to swim across the river in the shortest
time. He should swim:
(a) Due north (b) Due northeast (c) At an angle of 30° with the north (d) At an angle of 60° with
the north

The position-time graph of a particle is a parabola opening upwards (x t²). Its velocity-time
graph will be a:
(a) Straight line passing through the origin.
b) Parabola.
c) Horizontal straight line.
d) Straight line with a negative slope.

A ball is dropped from a height and another ball is thrown horizontally from the same height at
the same time. Which ball will hit the ground first (neglecting air resistance)?
(a) The dropped ball (b) The thrown ball (c) They will hit simultaneously (d) Depends on their
masses

A vector A is rotated by a small angle dθ without a change in its magnitude. The magnitude of
the change in the vector |ΔA| is:
(a) A dθ (b) 2A sin(dθ/2) (c) Zero (d) Both a and b are correct for small angles.

Section 2: Advanced Dynamics & Work-Energy

1. A block of mass 'm' is placed on a smooth wedge of inclination θ. The whole system is
accelerated horizontally so that the block does not slip on the wedge. The acceleration of the
system is:
(a) g sinθ (b) g cosθ (c) g tanθ (d) g cotθ

The potential energy of a particle is given by U(x) = 2x² - 8x. The particle is in stable equilibrium
at:
(a) x = 0 (b) x = 2 (c) x = 4 (d) x = -2

A chain of length L and mass M is lying on a smooth table with 1/3 of its length hanging over
the edge. The work done in pulling the entire chain onto the table is:
(a) MgL/3 (b) MgL/6 (c) MgL/9 (d) MgL/18

A particle of mass 'm' is driven by a machine that delivers a constant power 'P' watts. If the
particle starts from rest, its velocity 'v' at time 't' is proportional to:
(a) t (b) t² (c) √t (d) 1/√t

In a perfectly inelastic collision between two particles, which of the following is true for the
system?
(a) Both momentum and kinetic energy are conserved.
b) Momentum is conserved, but the maximum possible kinetic energy is lost.
c) Kinetic energy is conserved, but momentum is not.
d) Neither is conserved.

A bullet of mass 'm' hits a block of mass 'M' resting on a frictionless surface and gets
embedded in it. If the initial velocity of the bullet is 'v', the velocity of the combined system is:
(a) v (b) (M/m)v (c) (m/M)v (d) (m / (m+M))v

A force F = (-y i + x j) N acts on a particle. The force is:

(a) Conservative (b) Non-conservative (c) Frictional (d) Gravitational

Section 3: Advanced Rotational Dynamics

1. A solid cylinder, a hollow cylinder, a solid sphere, and a hollow sphere all of the same mass and
radius are released from the top of an inclined plane. The one with the largest acceleration
(reaching the bottom first) is the:
(a) Solid sphere (b) Hollow sphere (c) Solid cylinder (d) Hollow cylinder
 The moment of inertia of a body about a given axis is 1.2 kg·m². Initially, the body is at rest. In
order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/s²
must be applied about that axis for a duration of:
(a) 2 s (b) 4 s (c) 8 s (d) 10 s

A thin circular ring is rolling down an inclined plane without slipping. The ratio of its
translational kinetic energy to its rotational kinetic energy is:
(a) 1:1 (b) 2:1 (c) 1:2 (d) 5:2

The angular momentum of a particle is conserved if the:

(a) Net force on the particle is zero.
b) Net torque on the particle is zero.
c) Particle is moving in a straight line.
d) Particle is moving with constant velocity.

A turntable rotates with a constant angular velocity ω. A man of mass 'm' standing at the edge
of radius 'R' walks towards the center. The angular velocity of the system will:
(a) Decrease (b) Increase (c) Remain constant (d) Become zero

The instantaneous axis of rotation for a wheel rolling on a flat surface is:
(a) The center of the wheel. (b) The topmost point of the wheel. (c) The point of contact with
the ground. (d) A point in front of the wheel.

Torque is the rotational analogue of force. The work done by a torque is given by:
(a) W = τ × θ (b) W = τ . dθ (c) W = ∫ τ dθ (d) W = τ / θ

Section 4: Advanced SHM & Elasticity

1. The equation of motion for a damped harmonic oscillator is given by m(d²x/dt²) + b(dx/dt) + kx
= 0. The term responsible for damping is:
(a) m(d²x/dt²) (b) b(dx/dt) (c) kx (d) The entire equation

If a hole is drilled through the center of the Earth and a ball is dropped into it, the ball will
execute (assuming a uniform Earth and neglecting resistance):
(a) Uniform motion (b) Uniformly accelerated motion (c) Simple harmonic motion (d) Circular
motion

The total energy of a particle in SHM is E. The kinetic energy of the particle when its
displacement is half of the amplitude is:
(a) E/4 (b) E/2 (c) 3E/4 (d) E

Two simple pendulums of lengths in the ratio 4:1 have their time periods in the ratio:
(a) 4:1 (b) 1:4 (c) 2:1 (d) 1:2

For a mass 'm' attached to two springs of constant k₁ and k₂ in parallel, the time period of
oscillation is proportional to:
(a) √(m / (k₁k₂)) (b) √(m / (k₁+k₂)) (c) √(m(k₁+k₂) / k₁k₂) (d) √((k₁+k₂)/m)

The breaking force for a wire of diameter D is F. The breaking force for another wire of the
same material but diameter 2D is:
(a) F (b) 2F (c) 4F (d) F/2

The ratio of Young's modulus of a perfectly rigid body to that of a perfectly plastic body is:
(a) 1 (b) 0 (c) 0.5 (d) Infinite

The potential energy stored per unit volume in a stretched wire (elastic potential energy
density) is:
(a) Stress × Strain (b) ½ × Stress × Strain (c) Y × Strain (d) Stress / Strain

Section 5: Advanced Fluid Mechanics

1. A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the
top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is
completely filled with water, the quantities of water flowing out per second from both holes are
the same. Then, R is equal to:
(a) L/√2π (b) L/2π (c) L (d) 2πL

An object weighs 50 N in air and 40 N when fully immersed in water. The specific gravity of the
object is:
(a) 1.25 (b) 4 (c) 5 (d) 0.8

The velocity of efflux of a liquid from an orifice at a depth 'h' below the free surface is given by
Torricelli's law as:
(a) √(gh) (b) 2gh (c) √(2gh) (d) gh

The Reynolds number is a dimensionless quantity that is used to predict the:

(a) Viscosity of a fluid. (b) Onset of turbulent flow. (c) Surface tension of a fluid. (d) Buoyant
force.

A small drop of liquid splits into 8 identical smaller droplets. The total surface energy of the
system will:
(a) Decrease (b) Remain the same (c) Double (d) Quadruple

Bernoulli's equation is a statement of energy conservation for an ideal fluid in streamline flow.
The term P + ½ρv² + ρgh is:
(a) Constant (b) Zero (c) Always increasing (d) Always decreasing

The angle of contact for a liquid that wets the surface of a solid is:
(a) Acute (< 90°) (b) Obtuse (> 90°) (c) 90° (d) 180°

A Venturi meter is a device used to measure:

(a) Fluid pressure (b) Fluid density (c) Fluid viscosity (d) The speed of fluid flow

When a body attains terminal velocity, its net acceleration is:

(a) g (b) Zero (c) g/2 (d) -g

A hydraulic press works on Pascal's law. If the ratio of the areas of the output piston to the
input piston is 100:1, the mechanical advantage is:
(a) 1 (b) 10 (c) 100 (d) 0.01

Section 6: Advanced Gravitation & Final Challenge

1. The escape velocity from the surface of the Earth is 11.2 km/s. If the Earth's mass were
doubled and its radius were halved, the new escape velocity would be:
(a) 11.2 km/s (b) 22.4 km/s (c) 5.6 km/s (d) 44.8 km/s

The total energy of a satellite in an elliptical orbit:

(a) Is constant at all points.
b) Is maximum when it is farthest from the planet (apogee).
c) Is maximum when it is closest to the planet (perigee).
d) Varies with its speed.

A planet moves around the Sun. At the perigee (closest point), its speed is ________, and at the
apogee (farthest point), its speed is ________.
a) maximum; minimum
b) minimum; maximum
c) constant
d) zero; maximum

A person can jump 1.5 m high on Earth. On a planet where the acceleration due to gravity is
one-fourth that of Earth, they can jump to a height of:
(a) 1.5 m (b) 0.375 m (c) 6 m (d) 9 m

If R is the radius of the Earth, the height at which the acceleration due to gravity is 1/9th of its
 value at the surface is:
(a) R/2 (b) R (c) 2R (d) 3R

The time period of a geostationary satellite is 24 hours. The time period of another satellite
orbiting at a height twice that of the geostationary satellite will be:
(a) 48 hours (b) 24 hours (c) 24√8 hours (d) 12 hours

A black hole is an object whose:

(a) Density is infinite. (b) Gravitational field is so strong that even light cannot escape. (c)
Temperature is absolute zero. (d) It is a source of dark energy.

The gravitational potential energy of a body of mass 'm' at a height 'h' above the Earth's surface
is given by:
(a) mgh (b) -GMm/(R+h) (c) -GMm/R (d) GMm/R²

The weight of a body in a freely falling lift is:

(a) mg (b) > mg (c) < mg (d) Zero

The tidal forces are a result of the:

(a) Total gravitational force from the Moon and Sun.
b) The differential gravitational force exerted by the Moon and Sun across the Earth.
c) The Earth's rotation.
d) The Earth's magnetic field.

Two bodies of masses 'm' and '9m' are placed at a distance 'r'. The gravitational force is F. The
gravitational field is zero on the line joining them at a distance of ________ from 'm'.
(a) r/2 (b) r/3 (c) r/4 (d) 2r/3

Final Challenge: A uniform rod of length L is acted upon by two forces F₁ and F₂ at its ends
along its length. The Young's modulus is Y and the area of cross-section is A. The total
elongation of the rod is:
(a) (F₁ + F₂)L / AY (b) (F₁ + F₂)L / 2AY (c) (F₁L / AY) + (F₂L / AY) (d) The net force (F₁-F₂) must be
considered.
(This is a trick question. The tension in the rod is not uniform.) The correct approach involves
integration, but for CEE, the most likely intended answer assumes average tension or
recognizes complexity. We will revisit the solution.

Final Challenge: A block of wood floats in water with 2/3 of its volume submerged. When the
same block is placed in oil, it floats with 9/10 of its volume submerged. The ratio of the density
of oil to the density of water is:
(a) 3/20 (b) 2/3 (c) 20/27 (d) 27/20

Section 1: Advanced Collision Problems (Continued)

352. A ball of mass 'm' moving with velocity 'v' undergoes a head-on elastic collision with another
ball of mass '2m' at rest. The velocities of the first and second ball after collision are:
(a) -v/3, 2v/3 (b) -v, v (c) v/3, 2v/3 (d) -v/2, v/2

353. A bullet of mass 20 g strikes a sandbag of mass 5 kg and gets embedded in it. If the
sandbag moves with a velocity of 1 m/s, what was the initial kinetic energy of the bullet?
(a) 2.5 J (b) 25.1 J (c) 627.5 J (d) 1255 J

354. A ball is dropped from a height of 20 m. If the coefficient of restitution is 0.9, the height to
which the ball will rebound after the first bounce is:
(a) 18 m (b) 16.2 m (c) 14.4 m (d) 12 m

355. A body of mass 2 kg moving at 3 m/s collides with a body of mass 1 kg moving at 4 m/s in
the opposite direction. If they stick together, the velocity of the combined mass is:
(a) 2/3 m/s (b) -2/3 m/s (c) 10/3 m/s (d) -10/3 m/s

356. In an oblique collision of two identical spheres, where one is initially at rest, if the collision
is perfectly elastic, the angle between their final velocities will be:
(a) 0° (b) 45° (c) 90° (d) 180°
357. The loss of kinetic energy in an inelastic collision is primarily converted into:
(a) Potential energy (b) Light energy (c) Heat, sound, and deformation energy (d) Electrical energy

358. A radioactive nucleus at rest decays by emitting an alpha particle. The ratio of the kinetic
energy of the alpha particle to that of the recoiling daughter nucleus is: (M_d = mass of daughter,
M_α = mass of alpha)
(a) M_d / M_α (b) M_α / M_d (c) 1 (d) (M_d + M_α) / M_α

359. A cannonball fired from a cannon explodes in mid-air. The kinetic energy of the system
________ and the linear momentum ________.
a) increases; is conserved
b) is conserved; increases
c) increases; increases
d) is conserved; is conserved

360. A rubber ball and a clay ball of the same mass are thrown with the same speed against a
wall. The rubber ball bounces back, while the clay ball sticks. The change in momentum is
greater for the:
(a) Clay ball (b) Rubber ball (c) Both are the same (d) Cannot be determined

Section 2: Center of Mass Shift & System Dynamics

361. From a uniform circular disc of radius R, a smaller circular disc of radius R/2 is cut out with
its center at a distance R/2 from the center of the original disc. The center of mass of the
remaining portion is at a distance of ________ from the center of the original disc, on the side
opposite to the cutout.
(a) R/3 (b) R/4 (c) R/5 (d) R/6

362. Four particles of masses m, 2m, 3m, and 4m are placed at the four corners of a square of
side 'a'. The coordinates of the center of mass are: (Assume 'm' is at (0,0), '2m' at (a,0), '3m' at
(a,a), '4m' at (0,a))
(a) (a/2, a/2) (b) (5a/10, 7a/10) (c) (7a/10, 5a/10) (d) (a/10, a/10)

363. A man of mass 'M' is standing at one end of a boat of mass '2M' and length 'L' at rest in still
water. If the man walks to the other end of the boat, the distance moved by the boat is:
(a) L/2 (b) L/3 (c) 2L/3 (d) L

364. From a uniform square lamina of side 'a', a circular hole of maximum possible area is cut
out. The center of mass of the remaining portion will:
(a) Shift towards the hole (b) Shift away from the hole (c) Remain at the center (d) Shift to one of
the corners

365. Two blocks of masses 5 kg and 10 kg are connected by a light spring and are at rest on a
frictionless surface. If a constant force of 30 N is applied to the 10 kg block, what is the
acceleration of the center of mass of the system?
(a) 1 m/s² (b) 2 m/s² (c) 3 m/s² (d) 6 m/s²

366. A uniform rod of length L is bent at its midpoint to form a 90° angle. The distance of the
center of mass of the bent rod from the midpoint (the corner) is:
(a) L/4 (b) L√2 / 4 (c) L/8 (d) L√2 / 8

Section 3: Advanced Rotational Dynamics & Energy

367. A solid sphere rolls on a horizontal surface without slipping. The ratio of its rotational
kinetic energy to its total kinetic energy is:
(a) 2/5 (b) 2/7 (c) 5/7 (d) 1/2

368. A thin circular disc is rotating about its axis with constant angular velocity ω. A man gently
steps on the disc at the edge and stands there. Which of the following will be conserved?
(a) Kinetic energy only (b) Angular velocity (c) Angular momentum (d) Both KE and angular
momentum
369. If the radius of the Earth shrinks by 1% (mass remaining constant), the angular velocity of
the Earth's rotation will:
(a) Increase by ~2% (b) Decrease by ~2% (c) Increase by ~1% (d) Decrease by ~1%

370. The torque required to stop a wheel with a moment of inertia of 5 kg·m² from an angular
speed of 10 rad/s in 20 seconds is:
(a) 2.5 N·m (b) 5 N·m (c) 10 N·m (d) 20 N·m

371. A ladder is leaning against a smooth vertical wall and is resting on a rough horizontal floor.
The force of friction on the ladder from the floor acts:
(a) Towards the wall (b) Away from the wall (c) Vertically upwards (d) Vertically downwards

372. The physical quantity that is defined as the moment of linear momentum is:
(a) Torque (b) Angular impulse (c) Angular momentum (d) Power

Section 4: Advanced SHM, Elasticity & Fluids

373. The total energy of a particle executing SHM is E. The potential energy of the particle when
its displacement is half of the amplitude is:
(a) E/4 (b) E/2 (c) 3E/4 (d) E

374. A simple pendulum is oscillating inside a lift. If the cable of the lift breaks and it falls freely,
the time period of the pendulum will become:
(a) Zero (b) Infinite (c) Shorter (d) Longer

375. The equation of a wave is y = 10 sin(2πt - 0.01x). The velocity of the wave is:
(a) 100π m/s (b) 200π m/s (c) 10 m/s (d) 20 m/s

376. The breaking force for a wire of diameter D is F. The breaking force for another wire of the
same material but diameter 2D is:
(a) F (b) 2F (c) 4F (d) F/2

377. The potential energy stored per unit volume in a stretched wire is:
(a) Stress × Strain (b) ½ × Stress × Strain (c) Y × (Strain)² (d) Both b and c are correct.

378. When two soap bubbles of different radii are in communication with each other:
(a) Air flows from the larger bubble to the smaller bubble.
b) Air flows from the smaller bubble to the larger bubble.
c) The bubbles remain in equilibrium.
d) Air flows until their radii become equal.

379. The excess pressure inside a spherical liquid drop of radius 'r' and surface tension 'T' is
given by:
(a) T/r (b) 2T/r (c) 4T/r (d) T/2r

380. The excess pressure inside a soap bubble of radius 'r' and surface tension 'T' is:
(a) T/r (b) 2T/r (c) 4T/r (d) T/2r

381. The rate of flow of a liquid through a capillary tube (Poiseuille's formula) is proportional to
________, where 'r' is the radius of the tube.
(a) r (b) r² (c) r³ (d) r⁴

382. When a capillary tube is dipped in water, water rises to a height 'h'. If the length of the tube
above the water surface is made less than 'h', then:
(a) Water will not rise at all. (b) Water will overflow from the tube. (c) Water will rise up to the top
of the tube and the angle of contact will change. (d) The meniscus will become convex.

383. The work done in blowing a soap bubble of radius R is proportional to:
(a) R (b) R² (c) R³ (d) 1/R

Section 5: Final Integrated & Conceptual Challenge

384. A body of mass 'm' is moving in a horizontal circle of radius 'r' with a constant speed 'v'. The
work done in completing one full circle is:
(a) ½mv² (b) 2πr × (mv²/r) (c) Zero (d) mv²/r

385. Escape velocity from the Earth's surface depends on its mass (M) and radius (R) as:
(a) √(M/R) (b) √(M/R²) (c) M/R (d) √(R/M)

386. The time period of a satellite orbiting very close to the Earth's surface is approximately:
(a) 24 hours (b) 1 hour (c) 84.6 minutes (d) 27.3 days

387. A solid sphere, a disc, and a ring of the same mass and radius are rolling on a horizontal
surface with the same linear velocity. The one with the maximum total kinetic energy is the:
(a) Solid sphere (b) Disc (c) Ring (d) All have the same total kinetic energy.

388. A particle executes SHM with an amplitude A. The distance travelled by the particle in one
time period is:
(a) A (b) 2A (c) 4A (d) Zero

389. The ratio of the specific heats of a gas (γ = Cp/Cv) is related to the degrees of freedom (f)
by the relation:
(a) γ = 1 + f/2 (b) f = 1 + 2/γ (c) γ = 1 + 2/f (d) f = 2(γ - 1)

390. A "perfectly black body" is one that:

(a) Is black in color. (b) Absorbs all radiation incident upon it. (c) Reflects all radiation incident
upon it. (d) Transmits all radiation.

391. The rate of cooling of a body is directly proportional to the temperature difference between
the body and its surroundings. This is a statement of:
(a) Stefan's Law (b) Wien's Displacement Law (c) Newton's Law of Cooling (d) Kirchhoff's Law