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:
Show 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.
Both (A) and (R) are true and (R) is the correct explanation of (A).
(A) is true but (R) is false.
Both (A) and (R) are true, but (R) is NOT the correct explanation of (A).
Show Solution
The Correct Option isC
Solution and Explanation
- The formula for the time period \( T \) of a simple pendulum is \( T = 2\pi \sqrt{\frac{L}{g}} \), where \( L \) is the pendulum's length and \( g \) is the acceleration due to gravity. The time period is influenced by \( g \), which is calculated as \( g = \frac{GM}{R^2} \). Here, \( G \) represents the gravitational constant, \( M \) is the planet's mass, and \( R \) is its radius.- Given that the planet's mass and radius are 4 and 2 times that of Earth, respectively, \( g \) will be altered, consequently affecting the time period. Therefore, Assertion (A) is incorrect.- The mass of the pendulum remains constant, which means Reason (R) is correct.Accordingly, the correct option is \( \boxed{(3) (A) \text{ is true but } (R) \text{ is false.}} \).
