Question

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:

• A. remain unchanged
• B. increase
• C. decrease
• D. become erratic

Answer 1

Answer: (B)

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.