JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Elasticity & SHM

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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)Both (A) and (R) are true and (R) is the correct explanation of (A).✓ Correct
(C)(A) is true but (R) is false.
(D)(A) is false but (R) is true.

Answer: (B)

Solution

Time period of a simple pendulum:

T = 2 π \frac{l}{g}

Acceleration due to gravity decreases with height above the Earth's surface:

g_{h} = \frac{g _{0} R ^{2}}{( R + h ) ^{2}} < g_{0}

Since

T \propto 1/ g

, a smaller

g

at higher altitude gives a larger

T

; the pendulum runs slower (longer period) at the top of a mountain than at the base. The assertion is true.

The reason states

T

decreases as

g

increases (and vice versa), which follows directly from

T \propto g^{- 1/2}

, and is exactly the relation used to establish the assertion.

Both statements are true, and the reason correctly explains the assertion.

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Elasticity & SHM

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