Question

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R): \begin{itemize} \item[(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. \item[(R)] The mass of the pendulum remains unchanged at Earth and the other planet. \end{itemize} In light of the above statements, choose the correct answer from the options given below:

• A. (A) is false, but (R) is true.
• B. Both (A) and (R) are true and (R) is the correct explanation of (A).
• C. (A) is true but (R) is false.
• D. Both (A) and (R) are true, but (R) is NOT the correct explanation of (A).

Hint:

The time period of a simple pendulum depends on the acceleration due to gravity \( g \). Gravity is determined by the mass and radius of the planet.

Answer 1

The Correct Option is C

- The time period \( T \) of a simple pendulum is given by: \[ T = 2\pi \sqrt{\frac{L}{g}}, \] where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity. The time period depends on \( g \), which is given by \( g = \frac{GM}{R^2} \), where \( G \) is the gravitational constant, \( M \) is the mass of the planet, and \( R \) is its radius. - For the given planet with mass and radius 4 and 2 times that of the Earth, \( g \) will change, which means the time period will also change. Thus, Assertion (A) is false. - The mass of the pendulum does indeed remain the same, so Reason (R) is true. Thus, the correct answer is \( \boxed{(3) (A) \text{ is true but } (R) \text{ is false.}} \).