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:
Answer: (D) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
$g = \dfrac{GM}{R^2}$. On the planet:
$$g' = \frac{G(4M)}{(2R)^2} = g$$
Since $T = 2\pi\sqrt{l/g}$ and $g$ is unchanged, the period stays the same: (A) is true.
Mass is the same everywhere, so (R) is true. But the period of a simple pendulum does not depend on the bob's mass at all; the period is unchanged because $g$ is unchanged. So (R) is not the explanation of (A).
Solution by Sreeraj P, M.Sc Physics