Question

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. (a) Statement \(-1\) is true, statement \(-2\) is true; statement \(-2\) is the correct explanation of statement \(-1\) (b) Statement \(-1\) is true, statement \(-2\) is true but statement \(-2\) is not the correct explanation of statement \(-1\) (c) Statement \(-1\) is true, statement \(-2\) is false (d) Statement \(-1\) is false, statement \(-2\) is true (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\) Statement \(-1:\) Periodic time of a simple pendulum is independent of the mass of the bob. Statement \(-2:\) The restoring force does not depend on the mass of the bob. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\)

Short answer

(C) Statement \(-1\) is true, statement \(-2\) is false

Step-by-step solution

Analyze Statement 1

The periodic time of a simple pendulum is given by the formula \(T = 2\pi \sqrt{\frac {L}{g}}\), where \(T\) is the period, \(L\) is the length of the pendulum, and \(g\) is the acceleration due to gravity. As we can see from the formula, the period does not depend on the mass of the bob. Therefore, Statement 1 is true.

Analyze Statement 2

The equation for the restoring force acting on a pendulum bob in a simple pendulum system is \(F = -mgsin(\theta)\), where \(F\) is the restoring force, \(m\) is the mass of the bob, \(g\) is the acceleration due to gravity, and \(\theta\) is the angular displacement of the pendulum from its equilibrium position. As we can see from the equation, the restoring force does depend on the mass of the bob. Therefore, Statement 2 is false.

Check Explanation

As Statement 1 is true and Statement 2 is false, there is no need to check if Statement 2 explains Statement 1 since Statement 2 is not the correct explanation for Statement 1. Based on our analysis, the correct option is: (C) Statement \(-1\) is true, statement \(-2\) is false