A hollow metallic sphere filled with water is hung from a support by a long thread. A small hole is made at the bottom of the sphere and it is oscillated. How will the time period of oscillations be affected as water slowly flows out of the hole?

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The time period will increase at first, then decrease until the sphere is empty; finally the period will be the same as that when the sphere was full of water

The time period will keep decreasing until the sphere is empty

The time period will keep increasing until the sphere is empty

The time period will remain unchanged as water is flowing out

answer is D.

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Detailed Solution

The length of the pendulum (l) is the distance between the point of support and the centre of mass of the sphere. The centre of mass (CM) of a sphere is at its centre when it is empty and completely filled with water. The $CM$ falls below the centre of the sphere as the water flows out until the sphere is half full after which the CM begins to rise. Hence the effective length of the pendulum (and hence its time period) will increase at first and decrease until the sphere is empty when it becomes equal to the time period when the sphere was full of water.

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