Question

A simple pendulum consists of a hollow sphere filled with mercury. As the mercury begins to leak out slowly through a small hole at the bottom, the time period of the pendulum will

• A. decrease continuously until the sphere is empty.
• B. first increase and then decrease to the original value.
• C. remain constant throughout.
• D. increase continuously until the sphere is empty.

Hint:

The period depends on the distance from the support to the centre of mass, which first increases and then returns to the original value.

Answer 1

The Correct Option is B

Step 1: Key idea
The effective length is the distance to the centre of mass, and $T\propto\sqrt{l}$.

Step 2: Variation of the centre of mass
It starts at the geometric centre, moves lower as mercury drains, and comes back to the geometric centre when the sphere is empty.

Step 3: Result
So $T$ rises and then falls back to the initial value, option (B).

Final Answer:
The period increases first and finally returns to the original value. \[ \boxed{\text{(B) }\text{first increase and then decrease to the original value.}} \]