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: Idea
The effective length is set by the centre of mass of the bob together with the sand inside.

Step 2: Variation
The centre of mass goes lowest when about half the sand remains, then rises back as the bob empties.

Step 3: Result
So the period rises to a maximum and then returns to its original value.

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