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JEE Main 2025 Jan 29 Shift 1, Physics Q5: SHM in Pendulums

JEE Main2025Jan 29, Shift 1Physics
Q.

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:

  1. A

    Both (A) and (R) are true but (R) is not the correct explanation of (A).

  2. B

    Both (A) and (R) are true and (R) is the correct explanation of (A).

  3. C

    (A) is true but (R) is false.

  4. D

    (A) is false but (R) is true.

Solution

The acceleration due to gravity at height above the Earth's surface is , which decreases with

The time period of a simple pendulum is Hence increases as decreases. At the top of a mountain is smaller, so is longer than at the base.

Both statements are correct, and the inverse dependence on in Reason directly explains the increase in at altitude.

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