Physics - SHM Question with Solution | TestHub

The time period of a simple pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$, where $l$ is the effective length of the pendulum, measured from the point of suspension to the center of mass of the bob.

Initially, when the hollow sphere is completely filled with sand, the center of mass is at the center of the sphere.

As the sand starts leaking out from the small hole at the bottom, the center of mass of the remaining sand and the sphere shifts downwards. This increases the effective length $l$ of the pendulum. Since $T\propto \sqrt{l}$, the time period $T$ initially increases.

When the sand continues to drain and the sphere becomes completely empty, the center of mass shifts back to the geometric center of the hollow sphere. This decreases the effective length $l$ back to its original value, causing the time period $T$ to decrease back to its initial value.

Therefore, the time period $T$ first increases and then decreases.

Answer: T first increases and then decreases