Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R) : Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
In the light of the above statements, choose the most appropriate answer from the options given below:

The time period of a simple pendulum is given by:

• $$T = 2\pi \sqrt{\frac{L}{g}}$$

At the top of a mountain, the value of $g$ is less than at the base, because gravitational acceleration decreases with altitude according to:

• $$g' = g \left(1 - \frac{2h}{R}\right)$$

where:

• $h$ is the height of the mountain,
• $R$ is the radius of the Earth.

Since $g' < g$, the denominator in the formula increases, meaning $T$ increases.

The time period formula shows that $T$ is inversely proportional to $\sqrt{g}$:

• $$T \propto \frac{1}{\sqrt{g}}$$

If $g$ increases, $T$ decreases, and if $g$ decreases, $T$ increases.

This correctly explains why the time period is longer at the top of a mountain.