Kinetic and Potential Energy: NEET MCQs with Answers

15 free questions on Kinetic and Potential Energy for NEET (UG), starting with previous-year NEET and AIPMT questions. Try each one, then tap Show answer for the answer and a short explanation.

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Question 1

Previous-year question
A block of mass M suspended from a long wire of length L stretches it so that its length becomes (L + l). The elastic potential energy stored in the extended wire is [NEET 2019]
  1. Mgl
  2. MgL
  3. ½Mgl
  4. ½MgL
Show answer
Answer: (C) ½Mgl
Explanation: The tension grows uniformly from 0 to Mg as the extension grows from 0 to l, so the stored energy is the average force times the extension: U = ½Mgl.

Question 2

Previous-year question
Two similar springs P and Q have spring constants K_P and K_Q with K_P > K_Q. They are stretched first by the same amount (case a) and then by the same force (case b). The work done by the springs W_P and W_Q are related as [AIPMT 2015]
  1. W_P = W_Q in case (a); W_P = W_Q in case (b)
  2. W_P > W_Q in case (a); W_Q > W_P in case (b)
  3. W_P < W_Q in case (a); W_Q < W_P in case (b)
  4. W_P = W_Q in case (a); W_P > W_Q in case (b)
Show answer
Answer: (B) W_P > W_Q in case (a); W_Q > W_P in case (b)
Explanation: For the same extension, W = ½kx² ∝ k, so W_P > W_Q. For the same force, W = F²/2k ∝ 1/k, so now W_Q > W_P.

Question 3

Previous-year question
A force acting on a particle moving in a straight line varies with the particle's velocity as F = k/v, where k is a constant. The work done by this force in time t is [AIPMT 1993]
  1. (k/v²)·t
  2. 2kt
  3. kt
  4. 2kt/v²
Show answer
Answer: (C) kt
Explanation: From Newton's second law, m dv/dt = k/v ⟹ mv dv = k dt. Integrating: ½mv² = kt. Since the left side is exactly the kinetic energy gained, by the work–energy theorem W = ΔKE = ½mv² = kt.

Question 4

Previous-year question
Two masses of 1 g and 9 g are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is [AIPMT 1993]
  1. 1 : 9
  2. 9 : 1
  3. 1 : 3
  4. 3 : 1
Show answer
Answer: (C) 1 : 3
Explanation: For equal kinetic energies, p = √(2mK) ∝ √m. p₁/p₂ = √(1/9) = 1/3 Hence the ratio is 1 : 3.

Question 5

Previous-year question
A body of mass m, starting from rest, is acted upon by a constant force and travels a certain distance d. The kinetic energy it acquires is directly proportional to [AIPMT 1994]
  1. m
  2. √m
  3. 1/√m
  4. independent of m
Show answer
Answer: (D) independent of m
Explanation: By the work–energy theorem, KE acquired = work done = F × d. Since both F and d are given quantities, the kinetic energy is fixed at Fd regardless of the mass. (A lighter body simply reaches a higher speed to acquire the same energy.)

Question 6

Previous-year question
If the momentum of a body is increased by 50%, the percentage increase in its kinetic energy is [AIPMT 1995]
  1. 50%
  2. 100%
  3. 125%
  4. 200%
Show answer
Answer: (C) 125%
Explanation: K = p²/2m, so K ∝ p². p₂/p₁ = 150/100 = 1.5 K₂/K₁ = (1.5)² = 2.25 Percentage increase = (2.25 − 1) × 100 = 125%.

Question 7

Previous-year question
The potential energy between two atoms of a molecule is given by U(x) = a/x¹² − b/x⁶, where a and b are positive constants and x is the interatomic separation. The atom is in stable equilibrium when [AIPMT 1995]
  1. x = (2a/b)^(1/6)
  2. x = (11a/5b)^(1/6)
  3. x = 0
  4. x = (a/2b)^(1/6)
Show answer
Answer: (A) x = (2a/b)^(1/6)
Explanation: For equilibrium, F = −dU/dx = 0 : dU/dx = −12a/x¹³ + 6b/x⁷ = 0 ⟹ 12a/x¹³ = 6b/x⁷ ⟹ x⁶ = 2a/b ⟹ x = (2a/b)^(1/6). This is the familiar Lennard-Jones minimum, which is a point of stable equilibrium.
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Question 8

Previous-year question
A particle is projected at 45° to the horizontal and possesses kinetic energy K at the moment of projection. Its kinetic energy at the highest point will be [AIPMT 2001, 1997]
  1. K/√2
  2. K/2
  3. 2K
  4. K
Show answer
Answer: (B) K/2
Explanation: At the top the velocity is purely horizontal, v = u cos 45° = u/√2. K_top = ½m(u/√2)² = ½ × ½mu² = K/2.

Question 9

Previous-year question
Two bodies whose kinetic energies are in the ratio 4 : 1 are moving with equal linear momentum. The ratio of their masses is [AIPMT 1999]
  1. 1 : 2
  2. 1 : 1
  3. 4 : 1
  4. 1 : 4
Show answer
Answer: (D) 1 : 4
Explanation: K = p²/2m, so for equal momentum m ∝ 1/K. m₁/m₂ = K₂/K₁ = 1/4 Hence the ratio of masses is 1 : 4.

Question 10

Previous-year question
Two bodies of masses m and 4m are moving with equal kinetic energies. The ratio of their linear momenta is [AIPMT 1998, 1997, 1989]
  1. 1 : 2
  2. 1 : 4
  3. 4 : 1
  4. 1 : 1
Show answer
Answer: (A) 1 : 2
Explanation: For equal kinetic energies, p = √(2mK) ∝ √m. p₁/p₂ = √(m/4m) = 1/2 Hence the ratio is 1 : 2.

Question 11

Previous-year question
Springs A and B having spring constants k_A and k_B (with k_A = 2k_B) are stretched by applying forces of equal magnitude. If the energy stored in spring A is E_A, the energy stored in spring B will be [AIPMT 2001]
  1. 2E_A
  2. E_A/4
  3. E_A/2
  4. 4E_A
Show answer
Answer: (A) 2E_A
Explanation: For an applied force F, extension x = F/k and stored energy E = ½kx² = F²/2k. Thus E ∝ 1/k for equal forces. Since k_A = 2k_B, i.e. k_B = k_A/2 : E_B/E_A = k_A/k_B = 2 ⟹ E_B = 2E_A. The softer spring stores more energy under the same force.

Question 12

Previous-year question
A stone is projected at 45° to the horizontal with kinetic energy K. Its kinetic energy at the highest point of the trajectory is [AIPMT 2001]
  1. K/2
  2. K/√2
  3. K
  4. zero
Show answer
Answer: (A) K/2
Explanation: At the highest point the vertical velocity is zero and only the horizontal component u cos 45° survives. K_top = ½m(u cos 45°)² = K cos²45° = K × (1/√2)² = K/2.

Question 13

Previous-year question
If the kinetic energy of a body is raised by 300%, the percentage change in its momentum will be [AIPMT 2002]
  1. 100%
  2. 150%
  3. 265%
  4. 73.2%
Show answer
Answer: (A) 100%
Explanation: New kinetic energy, K′ = K + 3K = 4K. Since p = √(2mK), momentum ∝ √K : p′/p = √(4K/K) = 2 ⟹ p′ = 2p. Percentage increase = ((2p − p)/p) × 100 = 100%.

Question 14

Previous-year question
A stationary particle explodes into two fragments of masses m₁ and m₂ that fly apart in opposite directions with velocities v₁ and v₂. The ratio of their kinetic energies E₁/E₂ is [AIPMT 2003]
  1. 1
  2. m₁v₂/m₂v₁
  3. m₂/m₁
  4. m₁/m₂
Show answer
Answer: (C) m₂/m₁
Explanation: Initial momentum is zero, so m₁v₁ = m₂v₂ — the two fragments carry equal magnitudes of momentum. Using E = p²/2m with equal p : E₁/E₂ = m₂/m₁. The lighter fragment carries away the greater share of the energy.

Question 15

Previous-year question
A long spring is stretched by 2 cm and stores potential energy U. If the same spring is instead stretched by 10 cm, the potential energy stored in it will be [AIPMT 2003]
  1. U/5
  2. 5U
  3. 10U
  4. 25U
Show answer
Answer: (D) 25U
Explanation: U = ½kx², therefore U ∝ x². U′/U = (10/2)² = 25 ⟹ U′ = 25U.

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