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What will be the effect on the time period if the Wooden bob replaced with Metal bob

QUESTION:

The bob of a simple pendulum is made of wood. What will be the effect on the time period if the wooden bob is replaced by an identical bob of aluminum?


ANSWER

The time period of a simple pendulum(T) does not change, if the wooden bob is replaced by an identical bob of aluminum (of same mass or same dimension) because the time period of a simple pendulum is independent of the material of the bob for small amplitude of oscillation.

NOTE: If the wooden block is very big, if the wooden block replaced with metal bob of same mass will not effect the time period of the pendulum. but wooden block replaced with metal bob of same dimension, due to more moment of inertia to the metal bob time period increases slightly.

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