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Conservative and non-conservative forces: NEET MCQs with answers

50 questions on this topic of Work, Energy and Power (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. A particle of mass m is taken from point P to point Q in a region having both a conservative force F_c and a non-conservative force F_nc. If ΔK is the change in kinetic energy and ΔU is the change in potential energy, the work done by the non-conservative force W_nc is given by:

  1. W_nc = ΔK - ΔU
  2. W_nc = ΔK + ΔU
  3. W_nc = -ΔK - ΔU
  4. W_nc = ΔU - ΔK
Show answer and explanation

Answer: (B) W_nc = ΔK + ΔU

According to the work-energy theorem, W_total = W_c + W_nc = ΔK. Since conservative work is related to potential energy by W_c = -ΔU, substituting gives -ΔU + W_nc = ΔK, which yields W_nc = ΔK + ΔU = ΔE_mech.

medium

2. A block of mass 1 kg is projected up a rough inclined plane of inclination 30° with an initial kinetic energy of 40 J. It travels up along the incline, comes to instantaneous rest, and slides back down to the starting point. If the work done against friction during the upward journey is 10 J, what is the kinetic energy of the block when it returns to the starting point? (Assume the magnitude of friction is constant throughout).

  1. 20 J
  2. 30 J
  3. 10 J
  4. 0 J
Show answer and explanation

Answer: (A) 20 J

The total initial energy is 40 J. Gravity is conservative, so its net work over the round trip is zero. Friction is non-conservative and dissipates 10 J going up and another 10 J coming down (total dissipation = 20 J). By the work-energy theorem, Final KE = Initial KE - Total work against friction = 40 J - 20 J = 20 J.

hard

3. A central force acting on a particle has the mathematical form F→ = [C / r³] r̂, where C is a non-zero constant and r is the distance from the origin. Which statement correctly characterizes this force?

  1. It is conservative, and its potential energy function can be written as U(r) = C / (2r²).
  2. It is non-conservative because the curl of any inverse cube force is non-zero.
  3. It is non-conservative because the magnitude decreases with the inverse cube of distance.
  4. It is conservative, and its potential energy function can be written as U(r) = -C / (2r²).
Show answer and explanation

Answer: (A) It is conservative, and its potential energy function can be written as U(r) = C / (2r²).

Every central force of the form F→ = f(r) r̂ is strictly conservative. The potential energy is related to the force by F(r) = -dU/dr. Thus, dU = -F(r) dr = -(C/r³) dr. Integrating gives U(r) = -∫ (C/r³) dr = C / (2r²) (taking U(∞) = 0).

medium

4. Which of the following force fields is non-conservative in nature?

  1. F→ = (-y î + x ĵ) N
  2. F→ = (y î + x ĵ) N
  3. F→ = (3x² î + 4y ĵ) N
  4. F→ = (2x î + 3y² ĵ) N
Show answer and explanation

Answer: (A) F→ = (-y î + x ĵ) N

A two-dimensional force F→ = Fx î + Fy ĵ is conservative if ∂Fx/∂y = ∂Fy/∂x. For F→ = -y î + x ĵ, ∂Fx/∂y = -1 while ∂Fy/∂x = +1, which are unequal, confirming that the force field is non-conservative. For all other options, the cross-derivatives are strictly equal.

easy

5. Which of the following properties is strictly characteristic of a conservative force?

  1. The work done depends directly on the path length traversed by the object
  2. The work done is completely recoverable when the body returns to its initial state
  3. The force is always directed opposite to the instantaneous velocity vector
  4. The force necessarily causes dissipation of mechanical energy into heat
Show answer and explanation

Answer: (B) The work done is completely recoverable when the body returns to its initial state

For a conservative force, the work done in moving a particle between two points is path-independent and entirely stored as potential energy. Consequently, when the system returns to its initial state, all the energy expended can be completely recovered without dissipation.

hard

6. A block of mass 2 kg slides down an inclined plane of inclination 37° and length 5 m, starting from rest at the top. The coefficient of kinetic friction between the block and the incline is μ = 0.25. Given g = 10 m/s², sin 37° = 0.6, and cos 37° = 0.8, what is the change in the mechanical energy (ΔE) of the block-Earth system during the descent?

  1. -16 J
  2. -40 J
  3. -60 J
  4. -20 J
Show answer and explanation

Answer: (D) -20 J

The change in total mechanical energy equals the work done by the non-conservative frictional force: ΔE = W_nc = -f_k · s = -(μ m g cos 37°) · s. Substituting the given values: ΔE = -(0.25 × 2 × 10 × 0.8) × 5 = -(4) × 5 = -20 J.

medium

7. Which of the following mathematical expressions correctly represents a conservative force field?

  1. F→ = 3x²y î + x³ ĵ
  2. F→ = y² î + x² ĵ
  3. F→ = -y î + x ĵ
  4. F→ = 2y î + 3x ĵ
Show answer and explanation

Answer: (A) F→ = 3x²y î + x³ ĵ

For a 2D force field F→ = F_x î + F_y ĵ to be conservative, ∂F_x/∂y must equal ∂F_y/∂x. For F→ = 3x²y î + x³ ĵ, ∂F_x/∂y = 3x² and ∂F_y/∂x = 3x². Since the cross-derivatives are identical, the curl is zero and the force is conservative.

easy

8. A constant force F→ = (3 î + 4 ĵ) N displaces a particle from origin (0, 0) to point (2 m, 3 m) along path 1 (a straight line), and along path 2 (along x-axis then parallel to y-axis). The works done W₁ and W₂ satisfy:

  1. W₁ > W₂
  2. W₁ < W₂
  3. W₁ = W₂ = 25 J
  4. W₁ = W₂ = 18 J
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Answer: (D) W₁ = W₂ = 18 J

A spatially constant force is strictly conservative, making the work done path-independent. The displacement vector is Δr→ = 2 î + 3 ĵ m. Thus, W₁ = W₂ = F→ · Δr→ = (3)(2) + (4)(3) = 6 + 12 = 18 J.

easy

9. Which of the following forces cannot have a potential energy function associated with it?

  1. Restoring force of an ideal spring
  2. Electrostatic force between two stationary charges
  3. Newtonian gravitational attraction
  4. Viscous drag force in a fluid
Show answer and explanation

Answer: (D) Viscous drag force in a fluid

Potential energy can only be defined for conservative forces. Viscous drag is a dissipative, velocity-dependent non-conservative force, so no potential energy function can be associated with it.

medium

10. A 2 kg particle moves in a region where the potential energy is given by U(x, y) = (3x² + 4y²) J. If the particle is released from rest at (2 m, 1 m), what is the magnitude of the force acting on it at that initial position?

  1. 10 N
  2. √208 N
  3. 14.4 N
  4. 12 N
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Answer: (B) √208 N

The force components are Fx = -∂U/∂x = -6x and Fy = -∂U/∂y = -8y. At (2, 1), Fx = -12 N and Fy = -8 N. The magnitude of the force is F = √((-12)² + (-8)²) = √(144 + 64) = √208 N (approx 14.42 N).

easy

11. A particle of mass m is taken from height h₁ to height h₂ above the Earth's surface along three different arbitrary paths: a straight vertical line, a zigzag path, and a smooth helical path. If W₁, W₂, and W₃ represent the work done by the gravitational force along these respective paths, then:

  1. W₁ > W₂ > W₃
  2. W₁ < W₂ < W₃
  3. W₁ = W₂ = W₃
  4. W₁ = W₃ ≠ W₂
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Answer: (C) W₁ = W₂ = W₃

The gravitational force near the Earth's surface is a conservative force. The work done by any conservative force depends solely on the initial and final positions of the body and is completely independent of the path traversed. Therefore, W₁ = W₂ = W₃ = -mg(h₂ - h₁).

easy

12. An ideal spring of force constant k = 400 N/m is compressed by 0.1 m and then allowed to expand back to its natural unstretched length, propelling a 1 kg block. Which of the following statements is correct regarding this expansion process?

  1. The spring force does -2 J of work because it is conservative.
  2. The spring force is non-conservative because the spring returns to its original shape.
  3. The work done by the spring force depends on whether the expansion is slow or fast.
  4. The potential energy of the spring decreases by 2 J.
Show answer and explanation

Answer: (D) The potential energy of the spring decreases by 2 J.

The elastic potential energy initially stored in the spring is U = (1/2)k x² = 0.5 × 400 × (0.1)² = 2 J. As the spring returns to its natural length, this potential energy decreases to 0, meaning ΔU = -2 J. The work done by the conservative spring force is W = -ΔU = +2 J, which is independent of the rate of expansion.

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