Work, Energy, and Power — DPP 1

20 NEET questions from Work, Energy, and Power, with answers and explanations. Attempt it as a timed test to get scoring, accuracy breakdown and mistake tracking.

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1
A string is used to pull a block of mass m vertically up by a distance h at a constant acceleration $\frac { g } { 3 }$. The work done by the tension in the string is
  1. A $\frac { 2 } { 3 } m g h$
  2. B $\frac { - m g h } { 3 }$
  3. C mgh
  4. D $\frac { 4 } { 3 } m g h$
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Correct answer: D

2
A stone of mass 1 kg tied to a light string of length l = 10 m is whirling in a circular path in the vertical plane. If the ratio of the maximum to minimum tensions in the string is 3, find the speeds (in m/s) of the stone at the lowest and highest points, respectively.
  1. A $20 \sqrt { 2 } , 20$
  2. B $22 \sqrt { 2 } , 30 \sqrt { 2 }$
  3. C $30 \sqrt { 2 } , 22 \sqrt { 2 }$
  4. D $20,20 \sqrt { 2 }$
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Correct answer: A

3
If F = 2x$^{2}$ - 3x - 2, then choose the correct option.
  1. A $x = - \frac { 1 } { 2 }$ is position of stable equilibrium
  2. B x = 2 is position of stable equilibrium
  3. C $x = - \frac { 1 } { 2 }$ is position of unstable equilibrium
  4. D x = 2 is position of neutral equilibrium
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Correct answer: A

4
A particle moves along X-axis from x = 0 to x = 1 m under the influence of a force given by F = (3x$^{2}$ + 2x - 10) N. Work done in the process is
  1. A + 4 J
  2. B - 4 J
  3. C + 8 J
  4. D - 8 J
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Correct answer: D

5
Two springs of spring constant 3000 N/m and 5000 N/m, respectively, are stretched with the same force. They will have potential energy in the ratio
  1. A 3 : 5
  2. B 5 : 3
  3. C 25 : 9
  4. D 1 : 1
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Correct answer: B

6
A man standing on the edge of a roof of a 20 m tall building projects a ball of mass 100 gm vertically up with a speed of 10 ms$^{-1}$ and simultaneously throws another ball of same mass vertically down with the same speed. Find the kinetic energy of each ball when they reach the ground (g = 10 ms$^{-2}$).
  1. A 10, 10
  2. B 10, 20
  3. C 20, 10
  4. D 25, 25
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Correct answer: D

7
A force $\vec { F } = ( 2 \hat { i } + 3 \hat { j } + 2 \hat { k } ) \mathrm { N }$ acts on a particle of mass m. The particle starts from points A(1, 2, 1) m and moves to point B(3, 4, 3) m. What is the total work done by the force on the particle?
  1. A 14 J
  2. B 12 J
  3. C 16 J
  4. D 10 J
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Correct answer: A

8
A position dependent force F = 7 - 2x + 3x$^{2}$ newton acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5 m. The work done in joules is:
  1. A 70
  2. B 270
  3. C 35
  4. D 135
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Correct answer: D

9
A pump can take out 7200 kg of water per hour from a 100 m deep well. Calculate the power of the pump, assuming that its efficiency is 50%. (g = 10 m/s$^{2}$)
  1. A 2 KW
  2. B 4 KW
  3. C 6 KW
  4. D 8 KW
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Correct answer: B

10
A block of mass $m$ is placed at origin (0, 0) and a force F = (2x + 2) N, is applied on the block so that it reaches at some other point, P(5, 0) m. Find the work done by the force.
Work, Energy, and Power – NEET-6612
  1. A 35 J
  2. B 30 J
  3. C 15 J
  4. D 21 J
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Correct answer: A

11
A massive box is dragged along a horizontal floor by a rope. The rope makes an angle of $60 ^ { \circ }$ with the horizontal. Find the work done if the tension in the rope is 200 N and the box is moved through a distance of 20 m .
  1. A 500 J
  2. B 1000 J
  3. C 1500 J
  4. D 2000 J
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Correct answer: D

12
The momentum of a body is tripled. By what percentage does its kinetic energy increase?
  1. A 100%
  2. B 200%
  3. C 800%
  4. D 400%
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Correct answer: C

13
The displacement x of a body of mass 1 kg on smooth horizontal surface as a function of time t is given by $x = \frac { t ^ { 3 } } { 3 }$ (where x is in metres and t is in seconds). Find the work done by the external agent for the first one second.
  1. A 0.5 J
  2. B 1 J
  3. C 1.5 J
  4. D 2 J
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Correct answer: A

14
Kinetic Energy acquired by a mass m in travelling a certain distance d, starting from rest, under the action of a constant force F is
  1. A Directly proportional to $\sqrt { m }$
  2. B Directly proportional to m
  3. C Directly proportional to $\frac { 1 } { m }$
  4. D Independent of m
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Correct answer: D

15
An engine pumps water of density ρ, through a hose pipe. Water leaves the hose pipe of cross-sectional area A with a velocity v. Find the power of the engine.
  1. A ρAv$^{2}$
  2. B $\frac { 1 } { 2 } \rho \mathrm { Av } ^ { 3 }$
  3. C ρAv$^{4}$
  4. D ρAv
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Correct answer: B

16
A massless platform is kept on a light elastic spring as shown in figure. When a particle of mass 0.1 kg is dropped on the pan from a height of 0.24 m, the particle strikes the pan, and the spring is compressed by 0.01 m. From what height should the particle be dropped to cause a compression of 0.04 m?
Work, Energy, and Power – NEET-6680
  1. A 0.96 m
  2. B 2.96 m
  3. C 3.96 m
  4. D 0.48 m
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Correct answer: C

17
A body of mass 10 kg is released from the top of a tower which acquires as velocity of 10 m/s after falling through the distance of 20 m. Calculate the work done by the drag force of the air on the body? (take g = 10 m/s$^{2}$)
  1. A 1000 J
  2. B -1500 J
  3. C 2000 J
  4. D 2500 J
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Correct answer: B

18
Two bodies of masses m$_{1}$ and m$_{2}$ are moving with same kinetic energy. If P$_{1}$ and P$_{2}$ are their respective momentum, the ratio $\frac { P _ { 1 } } { P _ { 2 } }$ is equal to
  1. A $\frac { m _ { 1 } } { m _ { 2 } }$
  2. B $\sqrt { \frac { m _ { 2 } } { m _ { 1 } } }$
  3. C $\sqrt { \frac { m _ { 1 } } { m _ { 2 } } }$
  4. D $\frac { m _ { 1 } ^ { 2 } } { m _ { 2 } ^ { 2 } }$
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Correct answer: C

19
Find the work done by lifting force in lifting a stone of mass 10 kg from the ground to a height of 4 m .
  1. A 200 J
  2. B 400 J
  3. C 600 J
  4. D 800 J
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Correct answer: B

20
A stone weighing 0.5 kg tied to a rope of length 0.5 m revolves along a circular path in a vertical plane. The tension of the rope at the bottom point of the circle is 45 N . To what height will the stone rise (from the position of breaking of rope) if the rope breaks at the moment when the velocity is directed upwards? (g = 10 m/s$^{2}$)
  1. A 0.5 m
  2. B 1 m
  3. C 1.5 m
  4. D 2 m
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Correct answer: C

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