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 true because the acceleration due to gravity is less at higher altitudes (e.g., the top of a mountain) than at sea level. As gravity decreases, the time period of the pendulum increases because the time period \( T \) is given by: \[ T = 2\pi \sqrt{\frac{l}{g}} \] where \( l \) is the length of the pendulum and \( g \) is the acceleration due to gravity. Reason (R) is also true because the time period decreases as \( g \) increases, and this relationship is correctly stated. However, the reason does not fully explain the assertion, as the change in \( g \) due to altitude does not directly correlate with the pendulum’s time period in the manner implied by the reason. Thus, the correct answer is (1).