Given below are two statements: Statement I: In a perfectly inelastic collision of an isolated system, the total linear momentum is conserved but some kinetic energy is lost. Statement II: In an elastic collision, the total kinetic energy after the collision equals that before it, although kinetic energy is not conserved during the contact. Choose the correct answer.

Both Statement I and Statement II are correct

Statement I is incorrect but Statement II is correct

Both Statement I and Statement II are incorrect

Statement I is correct but Statement II is incorrect

Work, Energy and Power

25 NEET-UG practice questions on Work, Energy and Power, part of Physics. The first 25 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Medium
A force F = (3x² + 2) N, with x in metres, acts along the x-axis on a 1.5 kg block resting at x = 0 on a smooth surface. What is the speed of the block at x = 2 m?
1. A4 m/s
2. B16 m/s
3. C6.1 m/s
4. D4.6 m/s
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Answer: A · 4 m/s
Work = integral of F dx from 0 to 2 = [x³ + 2x] = 8 + 4 = 12 J. By the work-energy theorem, (1/2)(1.5)v² = 12, so v² = 16 and v = 4 m/s.
- B: This gives v², forgetting the square root.
- C: This uses the final force of 14 N over the whole 2 m.
- D: This takes the mean of the force at the two ends, which fails for a non-linear force.
Remember this
For a variable force, work is the integral of F dx, then use the work-energy theorem.
Question 2 · Hard
A 1 kg particle moves along the x-axis under a conservative force with potential energy U(x) = (2x² − 8x + 10) J, x in metres. Its total mechanical energy is 10 J. What are its maximum speed and the position where this occurs?
1. A2√2 m/s at x = 2 m
2. B√20 m/s at x = 2 m
3. C4 m/s at x = 4 m
4. D4 m/s at x = 2 m
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Answer: D · 4 m/s at x = 2 m
U is least where dU/dx = 4x − 8 = 0, so at x = 2 m, where U = 2 J. Then KE = 10 − 2 = 8 J, so (1/2)(1)v² = 8 and v = 4 m/s. Check: this is SHM with k = 4 N/m, ω = 2 rad/s and turning points x = 0 and 4 m (A = 2 m), so v = Aω = 4 m/s.
- A: This forgets the factor 1/2 in kinetic energy.
- B: This takes the minimum of U to be zero rather than 2 J.
- C: x = 4 m is a turning point, where the speed is zero.
Remember this
Speed is greatest where potential energy is least; turning points lie where U equals the total energy.
Question 3 · Easy
In 60 s, a pump lifts 300 kg of water through a height of 20 m. What is the minimum power it needs? Take g = 10 m/s².
1. A50 W
2. B1000 W
3. C60000 W
4. D100 W
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Answer: B · 1000 W
Work against gravity = mgh = 300 × 10 × 20 = 60000 J. Power = 60000/60 = 1000 W.
- A: This leaves out the height in the work.
- C: This is the work in joules, not divided by the time.
- D: This leaves out g in the work.
Remember this
Power is the rate of doing work, so always divide the work by the time taken.
Question 4 · Medium
A 0.5 kg stone on a 1 m string is whirled in a vertical circle, with just enough speed at the top to keep the string taut. Taking g = 10 m/s², what is the tension in the string at the lowest point?
1. A30 N
2. B15 N
3. C25 N
4. D5 N
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Answer: A · 30 N
At the top, tension is zero and v² = gL = 10. Energy conservation gives v² at the bottom = 10 + 4gL = 50. At the bottom, T = mg + mv²/L = 5 + 25 = 30 N, which is 6mg.
- B: This uses v² = 2gL at the bottom instead of 5gL.
- C: This leaves out the weight and keeps only mv²/L.
- D: This is the weight alone.
Remember this
For the minimum case, the tension at the lowest point is 6mg and the speed there is √(5gL).
Question 5 · Medium
Given below are two statements: Statement I: In a perfectly inelastic collision of an isolated system, the total linear momentum is conserved but some kinetic energy is lost. Statement II: In an elastic collision, the total kinetic energy after the collision equals that before it, although kinetic energy is not conserved during the contact. Choose the correct answer.
1. ABoth Statement I and Statement II are correct
2. BStatement I is incorrect but Statement II is correct
3. CBoth Statement I and Statement II are incorrect
4. DStatement I is correct but Statement II is incorrect
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Answer: A · Both Statement I and Statement II are correct
Linear momentum is conserved in every collision of an isolated system, while a perfectly inelastic collision loses the maximum kinetic energy consistent with this. In an elastic collision, some kinetic energy turns into deformation energy during contact and returns afterwards. So both statements are correct.
- B: Statement I is correct: momentum is conserved but kinetic energy is not.
- C: Both statements match the definitions of the two collision types.
- D: Statement II is correct: kinetic energy is stored briefly during contact.
Remember this
Elastic means initial and final kinetic energies are equal, not that kinetic energy is constant at every instant.
Question 6 · Medium
Given below are two statements: Statement I: On the potential energy curve shown, point R is a position of stable equilibrium. Statement II: A particle moving under this potential energy alone, released from rest at P, reaches S with non-zero kinetic energy. Choose the correct answer.
Figure: MedExams
1. AStatement I is incorrect but Statement II is correct
2. BBoth Statement I and Statement II are correct
3. CStatement I is correct but Statement II is incorrect
4. DBoth Statement I and Statement II are incorrect
Answer and explanation in LearnFree account
Question 7 · Hard
A small 1 kg block is released from rest at the top of the frictionless track, which ends in a vertical circular loop. With g = 10 m/s², what normal reaction does the track exert on the block at the top T of the loop?
Figure: MedExams
1. A10 N
2. B20 N
3. C0 N
4. D30 N
Answer and explanation in LearnFree account
Question 8 · Easy
Force along the direction of motion varies with position x as plotted. Calculate the work done by this force from x = 0 to x = 8 m.
Figure: MedExams
1. A20 J
2. B60 J
3. C40 J
4. D80 J
Answer and explanation in LearnFree account
Question 9 · Hard
A small block slides without friction down a track that ends in a vertical circular loop of radius R. It starts from rest at a height 3R above the lowest point of the loop. What normal force does the track exert on the block at the top of the loop? (m is the mass of the block.)
1. A7mg
2. B2mg
3. Cmg
4. DZero
Answer and explanation in LearnFree account
Question 10 · Medium
On a smooth horizontal surface, a 1 kg ball moving at 6 m/s makes a head-on elastic collision with a 2 kg ball at rest. What fraction of the first ball's kinetic energy is transferred to the second ball?
1. A2/3
2. B8/9
3. C1/9
4. D4/9
Answer and explanation in LearnFree account
Question 11 · Easy
Under a constant force F = (3î + 4ĵ) N, a body is displaced by d = (2î − ĵ) m. How much work does the force do?
1. A10 J
2. B2 J
3. C11.2 J
4. D−2 J
Answer and explanation in LearnFree account
Question 12 · Medium
In a ballistic-pendulum experiment, a bullet of mass 10 g moving horizontally at 400 m/s embeds itself in a wooden block of mass 990 g hanging at rest from long strings. Taking g = 10 m/s², to what height does the block rise?
1. A80 m
2. B0.8 m
3. C0.2 m
4. D1.6 m
Answer and explanation in LearnFree account
Question 13 · Medium
A particle moves along the x-axis where its potential energy is U(x) = x² − 4x, with U in joules and x in metres. Where is the particle in stable equilibrium, and what force acts on it at x = 3 m?
1. Ax = 0; +4 N
2. Bx = 4 m; −2 N
3. Cx = 2 m; −2 N
4. Dx = 2 m; +2 N
Answer and explanation in LearnFree account
Question 14 · Hard
A 2 kg block rests on a smooth horizontal floor, attached to a horizontal spring of force constant 300 N/m whose other end is fixed to a wall; the spring is at its natural length. A 1 kg block sliding at 6 m/s along the line of the spring strikes the 2 kg block and sticks to it. What is the maximum compression of the spring?
1. AAbout 0.14 m
2. B0.2 m
3. CAbout 0.12 m
4. DAbout 0.35 m
Answer and explanation in LearnFree account
Question 15 · Easy
A stone tied to a string is whirled in a horizontal circle at constant speed. How much work does the tension in the string do on the stone in one revolution?
1. ANegative, because the tension opposes outward motion
2. BPositive, because the tension pulls the stone inward
3. CZero, because the tension is always perpendicular to the velocity
4. DEqual to the kinetic energy of the stone
Answer and explanation in LearnFree account
Question 16 · Medium
A car of mass 1000 kg climbs a slope with sin θ = 1/20 at a steady 20 m/s against road and air resistance totalling 500 N. Taking g = 10 m/s², what power does its engine deliver?
1. A10 kW
2. B20 kW
3. C1 kW
4. D210 kW
Answer and explanation in LearnFree account
Question 17 · Easy
A pump raises 100 kg of water through a height of 10 m in 20 s. Taking g = 10 m/s², what is its output power?
1. A10 kW
2. B200 kW
3. C500 W
4. D50 W
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Question 18 · Easy
A force F = (2î + 3ĵ − k̂) N moves a body through a displacement d = (î + 2ĵ + 4k̂) m. How much work does the force do?
1. A8 J
2. B0 J
3. C4 J
4. D12 J
Answer and explanation in LearnFree account
Question 19 · Hard
A body starts from rest and is driven along a straight line by a machine that delivers constant power. Ignoring friction, how does its displacement depend on time t?
1. AProportional to t^(3/2)
2. BProportional to t²
3. CProportional to t
4. DProportional to t^(1/2)
Answer and explanation in LearnFree account
Question 20 · Medium
A bob hanging from a light inextensible thread 0.5 m long is given a horizontal push at its lowest point. Taking g = 10 m/s², what is the least speed that lets it go round the full vertical circle?
1. A√5 m/s
2. B5 m/s
3. C√20 m/s
4. D√10 m/s
Answer and explanation in LearnFree account
Question 21 · Medium
Two clay balls of equal mass, moving at equal speeds in opposite directions along a line, collide and stick together. Which statement describes the result?
1. AThe lump is at rest, and all the kinetic energy is lost
2. BThe lump moves at the common initial speed
3. CThe lump is at rest, and the kinetic energy is unchanged
4. DThe lump moves at half the initial speed
Answer and explanation in LearnFree account
Question 22 · Medium
A force F = 3x² newton (x in metres) acts on a particle along the x-axis. How much work does it do as the particle moves from x = 1 m to x = 3 m?
1. A26 J
2. B24 J
3. C30 J
4. D27 J
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Question 23 · Easy
The linear momentum of a body is doubled while its mass stays the same. By what factor does its kinetic energy change?
1. A8 times
2. B4 times
3. C2 times
4. D√2 times
Answer and explanation in LearnFree account
Question 24 · Medium
Assertion A: In an elastic collision, the kinetic energy of each colliding body is the same before and after the collision. Reason R: In an elastic collision, the total kinetic energy of the system before and after the collision is the same. Choose the correct answer.
1. AA is correct but R is not correct
2. BBoth A and R are correct and R is the correct explanation of A
3. CA is not correct but R is correct
4. DBoth A and R are correct but R is not the correct explanation of A
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Question 25 · Medium
A ball of mass m moving at speed v collides head-on and elastically with a stationary ball of mass 3m. What is the velocity of the first ball just after the collision?
1. AZero
2. Bv/4, opposite to its original direction
3. Cv/2, in its original direction
4. Dv/2, opposite to its original direction
Answer and explanation in LearnFree account

Work, Energy and Power

A force F = (3x² + 2) N, with x in metres, acts along the x-axis on a 1.5 kg block resting at x = 0 on a smooth surface. What is the speed of the block at x = 2 m?

A 1 kg particle moves along the x-axis under a conservative force with potential energy U(x) = (2x² − 8x + 10) J, x in metres. Its total mechanical energy is 10 J. What are its maximum speed and the position where this occurs?

In 60 s, a pump lifts 300 kg of water through a height of 20 m. What is the minimum power it needs? Take g = 10 m/s².

A 0.5 kg stone on a 1 m string is whirled in a vertical circle, with just enough speed at the top to keep the string taut. Taking g = 10 m/s², what is the tension in the string at the lowest point?

Given below are two statements: Statement I: On the potential energy curve shown, point R is a position of stable equilibrium. Statement II: A particle moving under this potential energy alone, released from rest at P, reaches S with non-zero kinetic energy. Choose the correct answer.

A small 1 kg block is released from rest at the top of the frictionless track, which ends in a vertical circular loop. With g = 10 m/s², what normal reaction does the track exert on the block at the top T of the loop?

Force along the direction of motion varies with position x as plotted. Calculate the work done by this force from x = 0 to x = 8 m.

A small block slides without friction down a track that ends in a vertical circular loop of radius R. It starts from rest at a height 3R above the lowest point of the loop. What normal force does the track exert on the block at the top of the loop? (m is the mass of the block.)

On a smooth horizontal surface, a 1 kg ball moving at 6 m/s makes a head-on elastic collision with a 2 kg ball at rest. What fraction of the first ball's kinetic energy is transferred to the second ball?

Under a constant force F = (3î + 4ĵ) N, a body is displaced by d = (2î − ĵ) m. How much work does the force do?

In a ballistic-pendulum experiment, a bullet of mass 10 g moving horizontally at 400 m/s embeds itself in a wooden block of mass 990 g hanging at rest from long strings. Taking g = 10 m/s², to what height does the block rise?

A particle moves along the x-axis where its potential energy is U(x) = x² − 4x, with U in joules and x in metres. Where is the particle in stable equilibrium, and what force acts on it at x = 3 m?

A stone tied to a string is whirled in a horizontal circle at constant speed. How much work does the tension in the string do on the stone in one revolution?

A car of mass 1000 kg climbs a slope with sin θ = 1/20 at a steady 20 m/s against road and air resistance totalling 500 N. Taking g = 10 m/s², what power does its engine deliver?

A pump raises 100 kg of water through a height of 10 m in 20 s. Taking g = 10 m/s², what is its output power?

A force F = (2î + 3ĵ − k̂) N moves a body through a displacement d = (î + 2ĵ + 4k̂) m. How much work does the force do?

A body starts from rest and is driven along a straight line by a machine that delivers constant power. Ignoring friction, how does its displacement depend on time t?

A bob hanging from a light inextensible thread 0.5 m long is given a horizontal push at its lowest point. Taking g = 10 m/s², what is the least speed that lets it go round the full vertical circle?

Two clay balls of equal mass, moving at equal speeds in opposite directions along a line, collide and stick together. Which statement describes the result?

A force F = 3x² newton (x in metres) acts on a particle along the x-axis. How much work does it do as the particle moves from x = 1 m to x = 3 m?

The linear momentum of a body is doubled while its mass stays the same. By what factor does its kinetic energy change?

Assertion A: In an elastic collision, the kinetic energy of each colliding body is the same before and after the collision. Reason R: In an elastic collision, the total kinetic energy of the system before and after the collision is the same. Choose the correct answer.

A ball of mass m moving at speed v collides head-on and elastically with a stationary ball of mass 3m. What is the velocity of the first ball just after the collision?