13 Jun 2026

Classical Mechanics Exam Quiz

Five standard classical mechanics MCQs for physics entrance practice.

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

These are original exam-style practice questions based on common GATE, CSIR-NET and JEST classical mechanics patterns.

Q: [GATE 2024 style] 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
EXPLAIN: The total energy is kinetic plus potential: $H=p^2/(2m)+kx^2/2$.
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Q: [CSIR-NET 2023 style] 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
EXPLAIN: If $\partial L/\partial q=0$, Lagrange's equation gives $d(\partial L/\partial \dot q)/dt=0$.
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Q: [JEST 2022 style] 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
EXPLAIN: Angular motion contributes the centrifugal term $L^2/(2mr^2)$.
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Q: [GATE 2021 style] 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
EXPLAIN: A stable equilibrium is a local minimum of potential energy, so the second derivative is positive.
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Q: [CSIR-NET 2020 style] The Poisson bracket $\{q,p\}$ equals
A: $0$
B: $1$
C: $-1$
D: $qp$
ANSWER: B
EXPLAIN: By definition, $\{q,p\}=(\partial q/\partial q)(\partial p/\partial p)-0=1$.

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