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 from the point of suspension to the center of mass of the bob.

Initially, the sphere is completely filled with mercury, so the center of mass is at the geometric center of the sphere.

As the mercury begins to leak out, the level of mercury falls, causing the center of mass of the system (sphere and remaining mercury) to shift downwards.

This downward shift increases the effective length $l$ of the pendulum, which in turn causes the time period $T$ to increase.

When the sphere becomes completely empty, the center of mass shifts back to the geometric center of the hollow sphere.

The effective length $l$ returns to its original value, and consequently, the time period $T$ decreases back to its original value.

Therefore, the time period first increases and then decreases to the original value.

Answer: first increase and then decrease to the original value.