13 Jun 2026

Classical Mechanics Standard Problems

Standard competitive exam problems in classical mechanics with answer key.

classical-mechanics gate-2024 csir-net-2023 jest-2022

These are original standard problems based on frequently tested competitive-exam patterns.

Q: For a one-dimensional harmonic oscillator, the Hamiltonian is
A: $p^2/(2m)+kx^2/2$
B: $px-kx$
C: $mv^2+kx$
D: $p^2/m+kx^2$
ANSWER: A
SOURCE: GATE 2024 style
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Q: If a coordinate is cyclic in the Lagrangian, its conjugate momentum is
A: zero
B: imaginary
C: conserved
D: equal to the force
ANSWER: C
SOURCE: CSIR-NET 2023 style
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Q: The effective potential for a particle in a central potential $V(r)$ is
A: $V(r)-L^2/(2mr^2)$
B: $V(r)+L^2/(2mr^2)$
C: $rV(r)$
D: $V(r)/r^2$
ANSWER: B
SOURCE: JEST 2022 style
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Q: For small oscillations, stable equilibrium requires
A: $d^2V/dq^2<0$
B: $d^2V/dq^2=0$
C: $d^2V/dq^2>0$
D: $V$ independent of $q$
ANSWER: C
SOURCE: GATE 2021 style
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Q: The Poisson bracket $\{q,p\}$ equals
A: $0$
B: $1$
C: $-1$
D: $qp$
ANSWER: B
SOURCE: CSIR-NET 2020 style
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Q: The moment of inertia of a point mass $m$ at distance $r$ from the rotation axis is
A: $mr$
B: $mr^2$
C: $m/r^2$
D: $r^2/m$
ANSWER: B
SOURCE: GATE style
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Q: Kepler's second law follows from conservation of
A: energy
B: linear momentum
C: angular momentum
D: mass
ANSWER: C
SOURCE: CSIR-NET style
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Q: For a particle constrained to move on a sphere, the number of generalized coordinates is
A: $1$
B: $2$
C: $3$
D: $4$
ANSWER: B
SOURCE: JEST style

Problem Sheet Standard MCQs