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Q.

A meter stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f0. If the bottom half of the stick were cut off if its new frequency of small oscillation is found to be xf0. The value of x is _____.

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answer is 2.

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Detailed Solution

We use f0=12πmglIwhere l is distance between point of suspension and centre of mass of the body.Thus, for the stick of length L and mass m frequency isf0=12πm⋅g⋅L2mL2/12=12π6gLwhen bottom half of the stick is cut off we usef1=12πm2⋅g⋅L4m2(L/2)212=12π×12gL=2f0Hence x = 2.
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