A rod pivoted at one of its end undergoes simple harmonic motion when given a small oscillation. If the pivot is changed such that its moment of inertia decreases to half of its original value, then its new time period is

Question

A rod pivoted at one of its end undergoes simple harmonic motion when given a  small oscillation. If the pivot is changed such that its moment of inertia decreases  to half of its original value, then its new time period is

Infinity Learn · Accepted Answer

For angular oscillation, angular $$frequency=$$  ω$$=cI$$    here $$c=couple$$ acting;  $$I=$$ moment of inertiaHence time $$period=$$ $$T=2$$$$π$$Ic …………………………(1)Since$$ time period is directly proportional to root of moment of inertia, the new time  period is T'$$=2$$$$π$$$$I2c$$ …………$$(2)Using$$ equation $$(1) and (2), it can be concluded that new time period is  T'$$=T2$$

A rod pivoted at one of its end undergoes simple harmonic motion when given a small oscillation. If the pivot is changed such that its moment of inertia decreases to half of its original value, then its new time period is

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