Question

12. A simple pendulum is made of a hollow spherical bob full of mercury and suspended by a thin string. If the mercury begins to leak from the small hole at its bottom, then its time period:

(a) Increases.                         (b) Decreases.

(c)First increases and then decreases till it is the same again

(d) First decreases and then increase still it is the same again

Answer 1

A simple pendulum is made with hollow sphere that has a hole at the bottom through which mercury that is filled in the sphere flows out gradually as the pendulum oscillates.

The time period of a simple pendulum made with a mass 'm' attached to a string of length 'L' is given by -

T = 2L / g

where, L = length from the point of suspension to a center of mass of the bob

If the mercury begins to leak from the small hole at its bottom, then its time period will be given as :

First increases and then decreases till it is the same again

Option (c) : it will be correct.

Explanation : Assuming the bob is spherical, as the mercury leaks out, the center of mass will shift downwards, increasing L and hence increasing the time period. As soon as all the mercury has leaked out, the center of mass will be back at the geometrical center, L will decrease and also will the time period.