JEE Physics 2025 Question with Solution

Given: Assertion (A): Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.

Find: Which option correctly evaluates Assertion (A) and Reason (R).

For a simple pendulum, the time period is

$$T = 2\pi \sqrt{\frac{l}{g}}$$

So, the time period decreases when the value of $g$ increases, and increases when the value of $g$ decreases.

At the top of a mountain, the acceleration due to gravity is smaller than at the base because the distance from the centre of the Earth is greater. Hence the value of $T$ becomes larger at the mountain top.

Therefore, Assertion (A) is true.

Reason (R) is also true because it correctly states the inverse dependence of time period on acceleration due to gravity.

However, Reason (R) gives only the general relation between $T$ and $g$. It does not state the specific cause that at the top of a mountain the value of $g$ decreases. Therefore, it is not the correct explanation of Assertion (A).

Thus, both (A) and (R) are true but (R) is not the correct explanation of (A).

The correct option is A.

Given:

• Assertion (A): The time period of a simple pendulum is longer at the top of a mountain than at the base of the mountain.
• Reason (R): The time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.

Find: Decide the correct relation between Assertion (A) and Reason (R).

1. Recall the formula for the time period of a simple pendulum:

$$T = 2\pi \sqrt{\frac{l}{g}}$$

where $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.

2. From the formula, $T$ is inversely proportional to $\sqrt{g}$.

3. At the top of a mountain, the value of $g$ decreases slightly compared to the base of the mountain.

4. When $g$ decreases, the value of $T$ increases.

5. Hence, the time period is longer at the top of a mountain. So Assertion (A) is true.

6. The Reason (R) is also true because increasing $g$ decreases the time period, and decreasing $g$ increases it.

7. But the reason does not directly mention that $g$ is smaller at higher altitude. So it does not fully explain why the time period is longer at the top of a mountain.

Therefore, both (A) and (R) are true but (R) is not the correct explanation of (A).

The correct option is A.