Question

The bob of a simple pendulum is a hollow sphere filled with water. How will the period of oscillation change if the water begins to drain off the hollow sphere?

Answer 1

Hint: We should know that a simple pendulum consists of a mass m hanging from a string of length L and fixed at a pivot point P. When displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion. The most commonly recognized use of pendulums is observed in clocks. Many clocks, most notably the grandfather clock, use a pendulum to tally time. The pendulum swings back and forth at exact intervals determined by the length at which the pendulum is suspended.

Complete step-by step answer:
We know that the time period is given as: $T=2\pi \sqrt{\dfrac{L}{g}}$
In the above expression:
l is the length from the point of suspension to the centre of mass of the bob and g is the acceleration due to gravity.
If water begins to drain out of the hollow sphere, its centre of mass begins to shift below the centre of the sphere. Hence the length of the pendulum increases, so time period increases.

So we can conclude that when the entire water is drained out of the sphere, the centre of mass shifts to the centre of the sphere and then time period attains its initial value.

Note: We should know that the time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing. One oscillation of a simple pendulum is one complete cycle of swinging one way and then returning to its original starting position. Pendulum, body suspended from a fixed point so that it can swing back and forth under the influence of gravity. Pendulums are used to regulate the movement of clocks because the interval of time for each complete oscillation, called the period, is constant.