Conservative Force — IISER Physics MCQs with Solutions
Free IISER 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. Depends on the speed of the particle
C. Is always positive
D. Is always zero
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 dx
B. F = +dU/dx
C. F = −dU/dx ✓ Correct
D. F = U/x
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. Depends on the loop's size
B. Zero ✓ Correct
C. +20 J
D. −20 J
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
D. −4 N ✓ Correct
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. +3 N ✓ Correct
B. −3 N
C. +9 N
D. Zero
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. Less negative than −20 J
B. Cannot be found without the path
C. More negative than −20 J
D. −20 J (same — path independent) ✓ Correct
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 · hard · theory
Friction is NOT a conservative force because:
A. The work it does around a closed path is non-zero (always negative) ✓ Correct
B. It is too weak
C. It cannot do positive work in any frame
D. It acts only on rough surfaces
Solution: Round any closed loop friction continually opposes motion, so ΣW < 0 ≠ 0 — path matters, hence non-conservative. (In some frames friction CAN do positive work, so that option is wrong.)
Q8 — Conservative Force · hard · numerical
The potential energy of a particle in a plane is U(x, y) = 3x² + 2y² (J). The magnitude of the force on it at the point (1, 1) m is:
A. 5 N
B. √13 N
C. √52 ≈ 7.2 N ✓ Correct
D. 10 N
Solution: F⃗ = −(∂U/∂x î + ∂U/∂y ĵ) = −(6x î + 4y ĵ) = −(6î + 4ĵ) at (1,1); |F| = √(36+16) = √52 ≈ 7.2 N.