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Chapter 10: Problem 1406

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) \(\mathrm{d}\)

Short Answer

Expert verified
The correct answer is \(\textbf{(D)}\): Statement 1 is false, and Statement 2 is true.

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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Most popular questions from this chapter

The equation for displacement of a particle at time \(t\) is given by the equation \(\mathrm{y}=3 \cos 2 \mathrm{t}+4 \sin 2 \mathrm{t}\). The periodic time of oscillation is \(\ldots \ldots \ldots \ldots\) (A) \(2 \mathrm{~s}\) (B) \(\pi \mathrm{s}\) (C) \((\pi / 2) \mathrm{s}\) (D) \(2 \pi \mathrm{s}\)

A wire having length \(\mathrm{L}\) is kept under tension between \(\mathrm{x}=0\) and \(\mathrm{x}=\mathrm{L}\). In one experiment, the equation of the wave and energy is given by $\mathrm{y}_{1}=\mathrm{A} \sin (\pi \mathrm{x} / \mathrm{L}) \sin \omega \mathrm{t}\( and \)\mathrm{E}_{1}$ respectively. In another experiment, it is \(\mathrm{y}_{2}=\mathrm{A} \sin\) \(\\{(2 \pi \mathrm{x}) / \mathrm{L}\\} \sin 2 \omega \mathrm{t}\) and \(\mathrm{E}_{2}\). Then........ (A) \(E_{2}=E_{1}\) (B) \(E_{2}=2 \mathrm{E}_{1}\) (C) \(\mathrm{E}_{2}=4 \mathrm{E}_{1}\) (D) \(E_{2}=16 \mathrm{E}_{1}\)

The amplitude for a S.H.M. given by the equation $\mathrm{x}=3 \sin 3 \mathrm{pt}+4 \cos 3 \mathrm{pt}\( is \)\ldots \ldots \ldots \ldots \mathrm{m}$ (A) 5 (B) 7 (C) 4 (D) \(3 .\)

A rocket is moving at a speed of \(130 \mathrm{~m} / \mathrm{s}\) towards a stationary target. While moving, it emits a wave of frequency $800 \mathrm{~Hz}$. Calculate the frequency of the sound as detected by the target. (Speed of wave \(=330 \mathrm{~m} / \mathrm{s}\) ) (A) \(1320 \mathrm{~Hz}\) (B) \(2540 \mathrm{~Hz}\) (C) \(1270 \mathrm{~Hz}\) (D) \(660 \mathrm{~Hz}\)

A small spherical steel ball is placed at a distance slightly away from the center of a concave mirror having radius of curvature \(250 \mathrm{~cm}\). If the ball is released, it will now move on the curved surface. What will be the periodic time of this motion? Ignore frictional force and take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$. (A) \((\pi / 4) \mathrm{s}\) (B) \(\pi \mathrm{s}\) (C) \((\pi / 2) \mathrm{s}\) (D) \(2 \pi \mathrm{s}\)
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