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) \(\mathrm{b}\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\) Statement \(-1:\) The periodic time of a S.H.O. depends on its amplitude and force constant. Statement \(-2:\) The elasticity and inertia decides the frequency of S.H.O. (A) a (B) \(b\) (C) c (D) \(\mathrm{d}\)

Step by step solution

01

Reviewing Statement 1

Let's evaluate Statement 1: "The periodic time of a S.H.O. depends on its amplitude and force constant." The periodic time (time taken for one complete oscillation) of a S.H.O. is given by the equation, \(T = 2\pi\sqrt{\frac{m}{k}}\), where \(m\) is the mass, and \(k\) is the force constant. The amplitude does not affect the periodic time. So Statement 1 is incorrect.

02

Reviewing Statement 2

Now let's evaluate Statement 2: "The elasticity and inertia decide the frequency of S.H.O." The frequency of a S.H.O. is given by the equation, \(f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}\), where \(k\) represents the elasticity (force constant) and \(m\) represents the inertia (mass) of the system. Statement 2 is correct.

03

Comparing Statements and Choosing the Correct Option

Since Statement 1 is false and Statement 2 is true, the correct answer is option (d): "Statement 1 is false, Statement 2 is true." So, the final answer is: \( \boxed{\textbf{(D)}} \)

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