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  4. A simple pendulum is made of a body which is a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of pendulum will:

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Q. A simple pendulum is made of a body which is a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of pendulum will:

AFMCAFMC 2006

Solution:

Length of simple pendulum $=$ Distance between point of suspension and centre of gravity of system .
On draining off a little mercury, the centre of gravity gets lowered, that is, the length of simple pendulum increases. The time period of simple pendulum is given by
$ T=2\pi \sqrt{\frac{l}{g}} $
$ \Rightarrow T\propto \sqrt{l} $
As length of simple pendulum increases, the time period increases.