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Question 30375
JEE Physics · Hard

Rigid Body Dynamics: Advanced — Rolling on Curved Surface MCQ

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Advanced — Rolling on Curved SurfaceHardQuestion 30375

Question

A small sphere rolls without slipping inside a spherical bowl (large radius R). Small oscillations about the lowest point have a time period analogous to a simple pendulum but with effective length:
  1. A
    R
  2. B
    R/2
  3. C
    5R/7
    Correct
  4. D
    7R/5

Correct answer

5R/7

Explanation

For a solid sphere (I = 2mR²/5) rolling inside a bowl of radius R: T = 2π√(5R_eff/(7g)). The effective length is 5R/7 (not R as for a simple pendulum).

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