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:

When dealing with pendulum motion, remember that the time period depends on the acceleration due to gravity. A lower value of \( g \) (at higher altitudes) results in a longer time period.

Answer 1

The Correct Option is A

Assertion (A) is accurate: gravitational acceleration diminishes at higher altitudes compared to sea level. This reduction in \( g \) directly increases a pendulum's time period, as \( T = 2\pi \sqrt{\frac{l}{g}} \). Reason (R) is also accurate; the inverse relationship between \( T \) and \( g \) is correctly stated, meaning \( T \) decreases as \( g \) increases. However, Reason (R) is not a complete explanation for Assertion (A), as the implied direct correlation between altitude-induced \( g \) changes and pendulum period is not fully established by the statement. Therefore, the correct response is (1).