JEE Main 2025 · 29 January · morning · Single correct · +4 / −1
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 true but (R) is false.
- (c) Both (A) and (R) are true and (R) is the correct explanation of (A) .
- (d) (A) is false but (R) is true.
Answer and solution
Answer (c) Both (A) and (R) are true and (R) is the correct explanation of (A) .
Solution
Physics sir · 4 steps
Climb the mountain, g gets smaller, and a smaller g means a slower swing.
- Period formula. For a simple pendulum of length L, the time period depends on g as follows.
T = 2π√(L/g) ⇒ T ∝ 1/√g
- Check the Reason. Since T ∝ 1/√g, a larger g gives a smaller T and a smaller g gives a larger T. So (R) is true.
- Check the Assertion. At height h, gₕ = g(R/(R+h))², which is less than g at the base. With the same L, a smaller g makes T longer at the top, so (A) is true.
- So. (A) is true only because g falls with height and T grows as g falls, which is exactly what (R) says. Both are true and (R) explains (A), so the answer is (c).
The idea to keep. Whenever a pendulum moves (up a mountain, down a mine, into a lift), ask only one thing: did the effective g go up or down? T moves the opposite way, as 1/√g.
Answer from the NTA final answer key. Solution by PrepWiser.