Question

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R): 
(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. 
(R) The mass of the pendulum remains unchanged at Earth and the other planet. 
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 \( \boxed{(3) (A) \text{ is true but } (R) \text{ is false.}} \).