Conservative Force — JEE Main Physics MCQs with Solutions
Free JEE Main Physics Conservative Force MCQs with step-by-step solutions (8 questions). Part of Work, Power and Energy. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Conservative Force · easy · theory
A force is conservative if the work it does:
A. Is independent of the path (zero over any closed loop) ✓ Correct
B. Is always zero
C. Depends on the speed of the particle
D. Is always positive
Solution: Path-independence (equivalently, zero net work around any closed path) defines a conservative force — gravity, spring and electrostatic forces qualify; friction does not.
Q2 — Conservative Force · medium · theory
The force associated with a potential energy function U(x) is given by:
A. F = U/x
B. F = +dU/dx
C. F = ∫U dx
D. F = −dU/dx ✓ Correct
Solution: F = −dU/dx: the force points "downhill" on the potential-energy curve, towards decreasing U.
Q3 — Conservative Force · easy · numerical
A 2 kg particle is carried around a full closed loop in a uniform gravitational field. The work done by gravity over the loop is:
A. −20 J
B. +20 J
C. Zero ✓ Correct
D. Depends on the loop's size
Solution: Gravity is conservative: over any closed path the net work is exactly zero.
Q4 — Conservative Force · medium · numerical
The potential energy of a particle is U(x) = 2x² (J). The force on it at x = 1 m is:
A. −2 N
B. +2 N
C. −4 N ✓ Correct
D. +4 N
Solution: F = −dU/dx = −4x; at x = 1, F = −4 N (directed towards the origin — a restoring force).
Q5 — Conservative Force · hard · numerical
For U(x) = x³ − 3x² (J), the force on the particle at x = 1 m is:
A. +9 N
B. −3 N
C. Zero
D. +3 N ✓ Correct
Solution: F = −dU/dx = −(3x² − 6x) = 6x − 3x². At x = 1: 6 − 3 = +3 N.
Q6 — Conservative Force · medium · numerical
Gravity does −20 J on a 1 kg block moved from A to B along path 1. Along a different path 2 from A to B, the work done by gravity is:
A. −20 J (same — path independent) ✓ Correct
B. More negative than −20 J
C. Cannot be found without the path
D. Less negative than −20 J
Solution: For a conservative force, W depends only on the end points: it is −20 J along every path from A to B.
Q7 — Conservative Force · medium · numerical
The potential energy is U(x) = (x² − 4x) J. The particle experiences zero force at x =
A. 2 m ✓ Correct
B. 4 m
C. 1 m
D. 0
Solution: F = −dU/dx = −(2x − 4) = 0 ⇒ x = 2 m (a potential minimum: stable point).
Q8 — Conservative Force · hard · numerical
A spring force F = −100x acts on a particle. The work done BY this conservative force as the particle moves from x = 0.2 m to x = 0 is:
A. +2 J ✓ Correct
B. Zero
C. −2 J
D. +4 J
Solution: W_cons = −ΔU = U(0.2) − U(0) = ½×100×0.04 − 0 = +2 J. Moving towards equilibrium, the spring force does positive work.