a hollow sphere filled with water is used as the bob of a pendulum. if water slowly leaks out of the bob how will the time period vary?

T =2pi(L/g)^1/2

time period is independent of mass of bob so it should not vary when the water leaks..

This same question was asked in kvpy 2010 paper and their answer key says T increases first and then decreases 

Dear Varsha,

Yes u are correct T increases first because centre of mass of hollow sphere ( with water ) is in the centre of the sphere but as the water leaks from it the centre of mass shifts downwards and hence T starts decreasing.

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