SECTION B
17 a) The time dependence of aphysical quantity P is given by P = Po exp , where a
is a constant and t is time, determine the dimension of constant a. .
b) Give the dimensional formula of intensity.
18. If t= Vx +4, then find (dxdt),-4.
19. Determine the angle between Y=+fand -14.
20. China wares are wrapped in straw paper before packing. Why ?
OR
Determine the angle through which a cyclist can bend w.r.t the vertical while negotiating a
curve safely.
21. Plot a graph showing the elastic potential and kinetic energy of block Aoscillating between -x
and + X.
SECTIONC
22. a) State the number of significant figures in 30.00 m and 6.200 x 10's.
b) The equation (P + a/V) (V- b) =Constant. Determine the units of a.
c) Express dimension of mass in terms of velocity (v), energy (E) and force (E) taken as
fundamental quantity.
23. a) Acceleration-time graph of a body is shown. The corresponding velocity-time graph of the
same body
b) Velocity-time (v-) graph for a moving object is shown in the figure. Total displacement of the
object
during the time interval when there is non-zero acceleration and retardation is
(4)
3
10 20 30
40 50 60
t(sec)
24. a) The
velocity of aprojectile
its velocity (in at the initial
m/s) at terminal point Ais (2i+ 3j) m/s. Determine
b) The Xand y point B.
c0ordinates of the particle
and y are in the at any time are x=5t - 2t and y=10t respectively, where x
meters andt is in
25 A seconds. Determine the acceleration of the particle at t-2s.
smooth block is released
to slide on a at rest
rough incline jis ntimes ason a 45 incline and then slide a distance d. If the time taken
coefficient of friction. large as that to slide than ona smooth incline, find the
26.. Why is it easier to pull a
lawn roller than to push it ?
Explain.
OR
Define angle of repose. Derive its relation with
the coefficient of limiting friction. Mention one
advantage and one disadvantage of
friction.
27. A body of mass m moving with speed v collides
elastically head- on with another body of mass m
initially at rest. Show that the moving body willcome to a stop as a result of this collision.
b)What is the angle between the two identical
dimension?
particles after they undergo elastic collision in two
28.a) Give an example of conservative and an example of
non-conservative force.
b) Springs A and B are identical except that Ais stiffer
than B. Ia which spring is more work
expended if they are stretched by the same amount ?
SECTION D
Ouestions 29 and 30 are Case Study Based Questions ,where each question carries
mark.
29. TOPIC: Weight in lift or elevator
The person of 60 kg is standing on a plattorm Scale balance kept on the floor of an elevator
Cab is capable of motion in up or down directon With eithera uniform velocity or a
constant acceleration. The value of velocily as Well as acceleration may be adiusted at any
(5)
suitable value. Newton's second law of motion can be applied for the motion of elevator
cab. Take g = 10 m/s.
(0). Observed weight of the person, when elevator is at rest, is
(A) 600 N (C) 900 N
(B) 300 N (D) 120N
(ü). Observed weight of the person, when elevator cab is moving
upward with a constant
velocity of 2 m/s, willbe
(A) 600 N (B) 450 N (C) 800 N (D) 500 N
(iii). Observed weight of the person, when
elevator cab is going downward with a
acceleration of g/4,will be
(A) 600 N (B) 300 N (C) 450 N (D) 750 N
(iv). If the elevator cab suddenly goes out of
order and starts falling freely under gravity
then
observed weight of the person willbe
(A)60 kg (B) 120 N (C) 30 N (D) Zero
30. UNIFORM CIRCULAR
MOTION
Uniform circular motion is an accelerated
motion. In uniform circular motion, the speed
of the body remains the same but the
direction of motion changes at every point. Fig
shows the different velocity vectors at different
positions of the particle. At each
position, the velocity vector is perpendicular to the radius vector r.
Thus the velocity of
the body changes continuously and due to the continuous
change in the direction of
motion of the body. As the rate of change of velocity is
acceleration, so a uniform circular
motion is an accelerated motion.
() A particle completed 4 rounds along a circular path. The
anglar displacement of the
particles is
(A) 3n (B) 4 n (C)5 x (D) 87
(ii) A particle completed 4 rounds along a circular path in 20
second. The angular
velocity of the particles is
(6)
0 Jai4 rad/s
(B) r/4 rad/s
(iii) Aparticle is
velocity 2n/5
moving along a (C) 2/S radls (D)Sx/4 rad/s
rad/s. The circular path of radius 14 cm and with an angular
(A) 1.76 m/s linear velocity of the particle is:
(v) The (B) 17.6 m/s
direction of centripetal acceleration of (C) 0.176 m/s (D) 176 m/s
(A) Along
theradius towards the a body moving along a circular path is :
(C) Along centre.
the tangent at (B) Along the radius outwards the centre.
any point.
(D) None of these.
31.a) State the SECTION E
resultant of twoparallelogram law of vector
and Qinclined at addition
vectors P and find the magnitude and direction of the
b) If A an angle =0° and =90 with each other.
+B-Cand A' BC
+ then prove that and IBF are perpendicular to each other (3+2)
OR
a) What is a
projectile ?
b) For what angle of projection of a
attained by the projectile equal ? projectile, are the horizontal range and maximum height
c) The maximum range of
projectile is 2/N3 times actual range. What is the
for the actual range ? angle of projection
32. a) What are concurrent forces ? (1+2+2)
Obtain a condition for the equilibrium of
forces. three concurrent
b) A weight W is suspended from the
mid-point of a
order to make the rope perfectly horizontal, determine therope, whose ends are at the same level. In
force applied to each of its ends.
c) A rope of mass 0.1 kg is connected at the
same height of two opposite walls. It is allowed to
hang under its own weight At the contact point
between the rope and the wall, the rope makes an
angle =10(very small) w.r.t horizontal. Determine the tension
in the rope at its midpoint
between the walls.
(2+1.5+1.5)
OR
en tor race track of radius r is banked ar angle .
The coefficient of friction between wheels of
race car and road is .
a) Derive the expression for maximum permissible speed to
avoid slipping.
b) Derive the expression for optimum speed ofcar to avoid wear and tear.
(7)
horizontal road
The coefficient of friction between the ground and the wheels of a car moving on a
of
is 0.5. If the car starts from rest, what is the minimum distance in which it can acquire a speed
(2.5+0.5 +2)
72 km/h?g= 10m/s.
33. a)Why a metal ball rebound better than a rubber ball?
b) What is coefficient of restitution. State its value for a perfectly inelastic collision
c) A large mass M moving with a velocity v collides head-on with a very small mass m at rest. If the
collision is elastic obtain an expression for energy lost by the large mass m. (Take M+m as M)
(1+1+3)
OR
a) Give an example each for positive work, negative work and zero work.
b) State the work- energy theorem for a constant force.
c) A woman pushes a trunk on a railway platform which has a rough surface. She supplies a
force of 100 N over a distance of 10m. Thereafter she gets tired and her applied force
reduces linearly wib distance to 50 N. The total distance by which the trunk has been
moved is 20 m. Plot the force applied by the woman, and the frictional force which is 50 Nis quven.
Calculate the work done by the two forces over 20 m.
(2++2)
F (N)
A
100
50
E
10m ¡20m x (m)
Friction H
(8)
