Question

The bob of a simple pendulum is a hollow sphere with a small hole in the bottom. It is filled with sand and set into oscillation. Its periodic time (T) is measured at regular intervals. As the sand starts coming out we find that.

• A. T increases with time
• B. T does not change with time
• C. T first decreases and then increases
• D. T first increases and then decreases

Hint:

The effective length depends on the position of the centre of mass of the bob and sand.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Time period is \(T=2\pi\sqrt{\dfrac{l}{g}}\), where l is the distance from the support to the centre of mass.

Step 2: Sand leaving
At first the centre of mass is at the centre of the sphere. As sand leaks, the centre of mass moves down, so l increases and T increases.

Step 3: Later stage
When most sand is gone, the centre of mass moves back up to the centre of the hollow sphere, so l and T decrease again.

Final Answer:
The time period first increases and then decreases. \[ \boxed{\text{(D) }\text{T first increases and then decreases}} \]