In: Physics
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
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.