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JEE MAIN 2025
22-01-2025 SHIFT-2
Question
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below :
Select the correct option:
A
(A) is true but (R) is false
B
Both (A) and (R) are true and (R) is the correct explanation of (A)
C
Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
D
(A) is false but (R) is true
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$$ \begin{aligned} & g=\frac{G M}{R^2} \\ & g^{\prime}=\frac{G(4 M)}{(2 R)^2}=g \end{aligned} $$ A is correct, $R$ is correct; but since $T=2 \pi \sqrt{\frac{\ell}{\mathrm{~g}}}$ doesn't depend on mass R doesn't explain A .
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