Question

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:

• A. Both (A) and (R) are true but (R) is not the correct explanation of (A)
• B. (A) is false but (R) is true
• C. Both (A) and (R) are true and (R) is the correct explanation of (A)
• D. (A) is true but (R) is false

Hint:

The time period of a simple pendulum is inversely related to the square root of the acceleration due to gravity.

Answer 1

The Correct Option is A

To resolve the issue, let's examine the provided statements:

• Assertion (A): A simple pendulum's time period is greater at a mountain's summit than at its base.
• Reason (R): The time period of a simple pendulum shortens as the acceleration due to gravity increases, and lengthens as it decreases.

The formula for the time period (T) of a simple pendulum is:
T = 2π√(L/g)
where L represents the pendulum's length and g denotes the acceleration due to gravity. This formula indicates an inverse relationship between the time period and the square root of g. At higher altitudes, such as a mountain summit, the value of g diminishes slightly due to increased distance from Earth's center. Consequently, the time period (T) is longer at the mountain summit than at its base. Thus, Assertion (A) is accurate.

Reason (R) correctly asserts that the time period shortens with increased g, which is mathematically sound. However, while this statement is true, it does not specifically explain why the time period is longer at a mountain summit. This phenomenon is caused by the reduction in g at higher altitudes, which is only indirectly related to the stated reason.

Therefore, the correct conclusion is: Both (A) and (R) are true, but (R) does not provide the correct explanation for (A).