Part CCSIR NET December 2024the-radial-inertia-term-vanishes-with-r-dot

The radial inertia term vanishes with r dot

Consider a particle of mass m which is moving on a surface due to gravity. Suppose the Lagrangian of the particle in the cylindrical coordinates is given by $L = (m /2) [(1 + 4 α^{2} r^{2})$ ṙ $^{2} + r^{2} θ$ ̇ $^{2}] - m α$ gr $^{2}$ , where $α$ is a positive constant, and g is the acceleration due to gravity. If the particle is in circular motion, then

A.| $θ$ ̇| $= 2/ (g α)$
B.| $θ$ ̇| $= 1/ (g α)$
C.| $θ$ ̇| $= 2 g α$ ✓
D.| $θ$ ̇| $= g α$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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The radial inertia term vanishes with r dot

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