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: Understanding the Concept
The time period of a simple pendulum is \(T=2\pi\sqrt{\frac{l}{g}}\), where \(l\) is the distance from the point of suspension to the centre of mass of the bob.

Step 2: While mercury leaks
The centre of mass starts at the centre of the sphere. As mercury flows out, the centre of mass of the sphere and remaining mercury shifts downwards, so \(l\) increases and \(T\) increases.

Step 3: After the minimum
When most of the mercury is gone, the centre of mass moves back upwards towards the centre of the empty sphere, so \(l\) and \(T\) decrease.

Step 4: Compare the options
The period first increases and then decreases to the original value, which is option (B).

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