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Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R).
Assertion (A): The time period of a simple pendulum is longer at the top of a mountain than at the base of the mountain.
Reason (R): The time period of a simple pendulum decreases with increasing value of the acceleration due to gravity and vice versa.

Asked in JEE Main 29th Jan 1st Shift 2025 · Pendulum as a probe of g

• (1) Both (A) and (R) are true and (R) is the correct explanation of (A)
• (2) Both (A) and (R) are true but (R) is not the correct explanation of (A)
• (3) (A) is true but (R) is false
• (4) (A) is false but (R) is true

Step-by-step solution

Why the other options are wrong

• (2) (R) is not a separate fact sitting alongside (A). The dependence of T on g is the whole reason the period lengthens on the mountain.
• (3) (R) is just T=2π√L/g put into words, so it is true.
• (4) (A) is true: g is smaller higher up, so the pendulum runs slower there.

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