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Assertion (A): A simple pendulum is taken to a planet whose mass is 4 times and radius 2 times those of the Earth. The time period of the pendulum is the same on the Earth and on the planet. Reason (R): The mass of the pendulum bob is unchanged on the Earth and on the other planet. In the light of the above statements, choose the correct answer.

Asked in JEE Main 22nd Jan 2nd Shift 2025 · Pendulum with changed g

• (1) (A) is false but (R) is true.
• (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) Both (A) and (R) are true and (R) is the correct explanation of (A).

Step-by-step solution

Why the other options are wrong

• (1) (A) is in fact true, because g comes out unchanged on that planet.
• (3) (R) is a true statement about the bob; it is simply not the reason.
• (4) The period is independent of the bob's mass, so (R) cannot explain why the periods agree.

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