Q. 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 :
A) (A) is false but (R) is true
B) (A) is true but (R) is false
C) Both (A) and (R) are true and (R) is the correct explanation of (A)
D) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
Explanation
[Solution by Dr. Abubacker] $g\propto\frac M{R^2}$: $g_p=\frac4{2^2}\,g=g$, so $T=2\pi\sqrt{l/g}$ is the same and (A) is true. The mass of a pendulum is indeed unchanged, so (R) is true, but the period does not depend on mass, so (R) does not explain (A). Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.