#### The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would Option 1) remain unchanged Option 2) increase towards a saturation value Option 3) first increase and then decrease to the original value Option 4) First decrease and then increase to the original value

As we learnt in

Time period of oscillation of simple pendulum -

- wherein

l = length of pendulum

g = acceleration due to gravity.

For a pendulum, $\inline T= 2\pi \sqrt{\frac{l}{g}}$where $\inline l$  Is measured upto centre of gravity. The centre of gravity of system is at centre of sphere when hole is plugged. When unplugged, water drains out. Centre of gravity goes on descending. When the bob becomes empty, centre of gravity is restored to centre.

$\inline \therefore$     Length of pendulum first increases, then decreases to original value.

$\inline \therefore$    T would first increase and then decrease to the original value.

Correct option is 3.

Option 1)

remain unchanged

This is an incorrect option.

Option 2)

increase towards a saturation value

This is an incorrect option.

Option 3)

first increase and then decrease to the original value

This is the correct option.

Option 4)

First decrease and then increase to the original value

This is an incorrect option.