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PHYSICS
JEE-Main | JEE-Advance | NEET | BOARDS
DPP/ CP04
B.Tech IIT Roorkee (AIR 23)
Ex. Faculty ALLEN CAREER INSTITUTE, KOP-13
TA
[1]

DPP - Daily Practice Problems

Chapter-wise Sheets
Date : Start Time : End Time :

PHYSICS CP05
SYLLABUS : Work, Energy and Power

Max. Marks : 180 Marking Scheme : (+4) for correct & (–1) for incorrect answer Time : 60 min.

INSTRUCTIONS : This Daily Practice Problem Sheet contains 45 MCQs. For each question only one option is correct.
Darken the correct circle/ bubble in the Response Grid provided on each page.

1. A spring of spring constant 5 × 10 3 N/m is stretched initially d d d

by 5cm from the unstretched position. Then the work (a) Mg (b) 3Mg (c) -3Mg (d) Mg d
required to stretch it further by another 5 cm is 4 4 4
(a) 12.50 Nm (b) 18.75 Nm 6. A rubber ball is dropped from a height of 5m on a plane,
(c) 25.00 Nm (d) 6.25 Nm where the acceleration due to gravity is not shown. On
2. A particle of mass 10 g moves along a circle of radius 6.4 cm bouncing it rises to 1.8 m. The ball loses its velocity on
with a constant tangential acceleration. What is the bouncing by a factor of
magnitude of this acceleration if the kinetic energy of the 16 2 3 9
particle becomes equal to 8 × 10–4 J by the end of the second (a) (b) (c) (d)
25 5 5 25
revolution after the beginning of the motion ?
7. A ball of mass m moving with a constant velocity strikes
(a) 0.1 m/s2 (b) 0.15 m/s2 (c) 0.18 m/s2 (d) 0.2 m/s2
against a ball of same mass at rest. If e = coefficient of
3. A body is moved along a straight line by a machine
restitution, then what will be the ratio of velocity of two
delivering a constant power. The distance moved by the
balls after collision?
body in time ‘t’ is proportional to
(a) t 3/4 (b) t 3/2 (c) t 1/4 (d) t 1/2 1- e e -1 1+ e 2+e
4. A ball is thrown vertically downwards from a height of 20 m (a) (b) (c) (d)
1+ e e +1 1- e e -1
with an initial velocity v0. It collides with the ground and 8. A particle of mass m is driven by a machine that delivers a
loses 50% of its energy in collision and rebounds to the constant power of k watts. If the particle starts from rest the
same height. The initial velocity v0 is : (Take g = 10 ms–2) force on the particle at time t is
(a) 20 ms–1 (b) 28 ms–1
(c) 10 ms–1 (d) 14 ms–1 (a) mk t –1/2 (b) 2mk t –1/2
5. A cord is used to lower vertically a block of mass M,
a distance d at a constant downward acceleration of g/4. 1 mk –1/2
(c) mk t –1/2 (d) t
The work done by the cord on the block is 2 2

RESPONSE 1. 2. 3. 4. 5.
GRID 6. 7. 8.
Space for Rough Work
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9. A body of mass 2 kg moving under a force has relation 15. The relationship between the force F and position x of a
body is as shown in figure. The work done in displacing the
t3
between displacement x and time t as x = where x is in body form x = 1 m to x = 5 m will be
3
F(N)
metre and t is in sec. The work done by the body in first two
10
second will be
(a) 1.6 joule (b) 16 joule 5
(c) 160 joule (d) 1600 joule
0 x(m)
10. A sphere of mass 8m collides elastically (in one dimension) l 2 3 4 5 6
with a block of mass 2m. If the initial energy of sphere is E. –5
What is the final energy of sphere?
(a) 0.8 E (b) 0.36 E –10
(c) 0.08 E (d) 0.64 E (a) 30 J (b) 15 J (c) 25 J (d) 20 J
11. Two similar springs P and Q have spring constants K P and 16. A body is allowed to fall freely under gravity from a height
KQ, such that KP > KQ. They are stretched, first by the same of 10m. If it looses 25% of its energy due to impact with the
amount (case a,) then by the same force (case b). The work ground, then the maximum height it rises after one impact is
done by the springs WP and WQ are related as, in case (a)
(a) 2.5m (b) 5.0m (c) 7.5m (d) 8.2m
and case (b), respectively
(a) WP = WQ ; WP = WQ (b) WP > WQ ; WQ > WP 17. A block C of mass m is moving with velocity v0 and collides
(c) WP < WQ ; WQ < WP (d) WP = WQ ; WP > WQ elastically with block A of mass m and connected to another
12. In the figure, the variation of potential energy of a particle block B of mass 2m through spring constant k. What is k if
of mass m = 2 kg is represented w.r.t. its x-coordinate. The x0 is compression of spring when velocity of A and B is
particle moves under the effect of this conservative force same?
along the x-axis. C v0 A B `
U (in J)
mv02 mv02
20
(a) (b)
15 x 02 2x 02
10
2 2
3 mv0 2 mv0
–5 5 (c) (d)
–10 2 10
X (in meter)
2 x 02 3 x 02
18. Two springs of force constants 300 N/m
–12 (Spring A) and 400 N/m (Spring B) are joined together in
series. The combination is compressed by 8.75 cm. The ratio
–15
E E
of energy stored in A and B is A . Then A is equal to :
If the particle is released at the origin then EB EB
(a) it will move towards positive x-axis 4 16 3 9
(b) it will move towards negative x-axis (a) (b) (c) (d)
(c) it will remain stationary at the origin 3 9 4 16
(d) its subsequent motion cannot be decided due to lack 19. A body of mass 1 kg begins to move under the action of a
r
of information time dependent force F=(2ti +3t 2 j) N, where i and j are
13. The potential energy of a certain spring when stretched unit vectors alogn x and y axis. What power will be developed
through distance S is 10 joule. The amount of work done (in by the force at the time t?
joule) that must be done on this spring to stretch it through (a) (2t2 + 3t3)W (b) (2t2 + 4t4)W
an additional distance s, will be 3 4
(c) (2t + 3t ) W (d) (2t3 + 3t5)W
(a) 20 (b) 10 (c) 30 (d) 40
14. A force applied by an engine of a train of mass 2.05×10 6 kg 20. A bullet of mass 20 g and moving with 600 m/s collides with
changes its velocity from 5m/s to 25 m/s in 5 minutes. The a block of mass 4 kg hanging with the string. What is the
power of the engine is velocity of bullet when it comes out of block, if block rises
(a) 1.025 MW (b) 2.05 MW to height 0.2 m after collision?
(c) 5 MW (d) 6 MW (a) 200 m/s (b) 150 m/s (c) 400 m/s (d) 300 m/s

9. 10. 11. 12. 13.

RESPONSE
14. 15. 16. 17. 18.
GRID
19. 20.
Space for Rough Work
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21. A body of mass m kg is ascending on a smooth inclined m/2
m
æ 1ö
plane of inclination q ç sin q = ÷ with constant acceleration /////////////////////////////////////////////////////////////
è xø d
of a m/s2. The final velocity of the body is v m/s. The work (a) 2 (b) 3 (c) 4 (d) 5
done by the body during this motion is 27. A force acts on a 30 gm particle in such a way that the
(Initial velocity of the body = 0) position of the particle as a function of time is given by x =
1 mv2 æ g ö 3t – 4t2 + t3, where x is in metres and t is in seconds. The
(a) mv2 (g + xa) (b) ç + a÷ work done during the first 4 seconds is
2 2 è2 ø (a) 576mJ (b) 450mJ (c) 490mJ (d) 530mJ
2mv 2 x mv 2 28. A particle of mass m1 moving with velocity v strikes with a
(c) ( a + gx ) (d) ( g + xa ) mass m2 at rest, then the condition for maximum transfer of
a 2ax
kinetic energy is
22. A glass marble dropped from a certain height above the
(a) m1 >> m2 (b) m2 >> m2 (c) m1 = m2 (d) m1 = 2m2
horizontal surface reaches the surface in time t and then
29. A mass m is moving with velocity v collides inelastically
continues to bounce up and down. The time in which the with a bob of simple pendulum of mass m and gets embedded
marble finally comes to rest is into it. The total height to which the masses will rise after
é1+ e ù é1 - e ù collision is
(a) en t (b) e2 t tê
(c) ú (d) t ê ú
ë1 - e û ë1 + e û v2 v2 v2 2v 2
(a) (b) (c) (d)
23. The potential energy of a 1 kg particle free to move along 8g 4g 2g g
æ x4 x2 ö 30. A 10 H.P. motor pumps out water from a well of depth 20 m
the x-axis is given by V( x) = ç - ÷ J. and fills a water tank of volume 22380 litres at a height of
ç 4 2 ÷ 10 m from the ground. The running time of the motor to fill
è ø
The total mechanical energy of the particle is 2 J. Then, the the empty water tank is (g = 10ms–2)
maximum speed (in m/s) is (a) 5 minutes (b) 10 minutes
(c) 15 minutes (d) 20 minutes
3 1
(a) (b) (c) (d) 2 31. A particle of mass m1 is moving with a velocity v1 and
2 2 2 another particle of mass m2 is moving with a velocity v2.
24. Water falls from a height of 60 m at the rate of 15 kg/s to Both of them have the same momentum but their different
operate a turbine. The losses due to frictional force are 10% kinetic energies are E1 and E2 respectively. If m1 > m2 then
of energy. How much power is generated by the turbine?( g E1 m1
= 10 m/s2) (a) E1 = E2 (b) E1 < E2 (c) E = m (d)E1 > E2
2 2
(a) 8.1 kW (b) 10.2 kW (c) 12.3 kW (d) 7.0 kW
32. A block of mass 10 kg, moving in x direction with a constant
24. A car of mass m starts from rest and accelerates so that the
speed of 10 ms–1, is subject to a retarding force F = 0.1 × J m
instantaneous power delivered to the car has a constant during its travel from x = 20 m to 30 m. Its final KE will be :
magnitude P0. The instantaneous velocity of this car is (a) 450 J (b) 275 J (c) 250 J (d) 475 J
proportional to : 33. Identify the false statement from the following
t (a) Work-energy theorem is not independent of Newton's
(a) t 2P 0 (b) t 1/2 (c) t –1/2 (d) second law.
m
(b) Work-energy theorem holds in all inertial frames.
25. When a 1.0kg mass hangs attached to a spring of length 50 (c) Work done by friction over a closed path is zero.
cm, the spring stretches by 2 cm. The mass is pulled down (d) No potential energy can be associated with friction.
until the length of the spring becomes 60 cm. What is the 34. A one-ton car moves with a constant velocity of
amount of elastic energy stored in the spring in this 15 ms–1 on a rough horizontal road. The total resistance to
condition. if g = 10 m/s2. the motion of the car is 12% of the weight of the car. The
(a) 1.5 joule (b) 2.0 joule(c) 2.5 joule (d) 3.0 joule power required to keep the car moving with the same constant
26. A block of mass m rests on a rough horizontal surface velocity of 15ms–1 is [Take g = 10 ms–2]
(Coefficient of friction is µ). When a bullet of mass m/2 (a) 9 kW (b) 18 kW (c) 24 kW (d) 36 kW
strikes horizontally, and get embedded in it, the block moves 35. A ball is released from the top of a tower. The ratio of work
a distance d before coming to rest. The initial velocity of the done by force of gravity in first, second and third second of
bullet is k 2mgd , then the value of k is the motion of the ball is
(a) 1 : 2 : 3 (b) 1 : 4 : 9 (c) 1 : 3 : 5 (d) 1 : 5 : 3

21. 22. 23. 24. 25.

RESPONSE 26. 27. 28. 29. 30.
GRID 31. 32. 33. 34. 35.
Space for Rough Work
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36. Two spheres A and B of masses m1 and m2 respectively 42. A block of mass M is kept on a platform which is accelerated
collide. A is at rest initially and B is moving with velocity v upward with a constant acceleration 'a' during the time
v interval T. The work done by normal reaction between the
along x-axis. After collision B has a velocity in a direction block and platform is
2
perpendicular to the original direction. The mass A moves
after collision in the direction. M a
(a) Same as that of B
(b) Opposite to that of B
(c) q = tan–1 (1/2) to the x-axis
(d) q = tan–1 (–1/2) to the x-axis MgaT 2 1
(a) - (b) M (g + a) aT 2
37. A 2 kg block slides on a horizontal floor with a speed of 4m/s. 2 2
It strikes a uncompressed spring, and compresses it till the 1
block is motionless. The kinetic friction force is 15N and spring (c) Ma 2 T (d) Zero
constant is 10,000 N/m. The spring compresses by 2
(a) 8.5 cm (b) 5.5 cm (c) 2.5 cm (d) 11.0 cm 43. A spring lies along an x axis attached to a wall at one end
38. An engine pumps water through a hose pipe. Water passes and a block at the other end. The block rests on a frictionless
through the pipe and leaves it with a velocity of 2 m/s. The surface at x = 0. A force of constant magnitude F is applied
mass per unit length of water in the pipe is 100 kg/m. What to the block that begins to compress the spring, until the
is the power of the engine? block comes to a maximum displacement xmax.
(a) 400 W (b) 200 W (c) 100 W (d) 800 W
39. A uniform chain of length 2 m is kept on a table such that a
length of 60 cm hangs freely from the edge of the table. The Energy 1
4
total mass of the chain is 4 kg. What is the work done in of work 2
pulling the entire chain on the table ?
(a) 12 J (b) 3.6 J (c) 7.2 J (d) 1200 J 3
40. A mass ‘m’ moves with a velocity ‘v’ and collides inelastically x
xmax
with another identical mass. After collision the lst mass moves During the displacement, which of the curves shown in the
v graph best represents the kinetic energy of the block ?
with velocity in a direction perpendicular to the initial (a) 1 (b) 2 (c) 3 (d) 4
3 44. The K.E. acquired by a mass m in travelling a certain distance
direction of motion. Find the speed of the 2nd mass after
collision. d, starting form rest, under the action of a constant force is
directly proportional to
v m m (a) m (b) m
3 A before 1
Aafter (c) (d) independent of m
collision collision m
2 45. A vertical spring with force constant k is fixed on a table. A
v
(a) 3 v (b) v (c) (d) v ball of mass m at a height h above the free upper end of the
3 3 spring falls vertically on the spring so that the spring is
41. A spherical ball of mass 20 kg is stationary at the top of a hill compressed by a distance d. The net work done in the
of height 100 m. It rolls down a smooth surface to the ground, process is
then climbs up another hill of height 30 m and finally rolls 1 1
down to a horizontal base at a height of 20 m above the (a) mg(h + d) - kd 2 (b) mg(h - d) - kd 2
ground. The velocity attained by the ball is 2 2
1 1
(a) 20 m/s (b) 40 m/s (c) 10 30 m/s (d) 10 m/s (c) mg(h - d) + kd 2 (d) mg(h + d) + kd2
2 2
RESPONSE 36. 37. 38. 39. 40.
GRID 41. 42. 43. 44. 45.

DAILY PRA CTICE PROBLEM DPP CHAPTERWISE CP05 - PHYSICS

Total Ques tions 45 Total Marks 180
Attempted Correct
Incorrect Net Score
Cut-off Score 50 Qualifying Score 70
Succes s Gap = Net Score – Space
Qualifying
for RoughScore
Work
Net Score = (Correct × 4) – (Incorrect × 1)
Space for Rough Work