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Chapter 4: Problem 534

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it. (1) If both assertion and reason and the reason is the correct explanation of the Assertion. (2) If both assertion and reason are true but reason is not the correct explanation of the assertion. (3) If the assertion is true but reason is false. (4) If the assertion and reason both are false. Assertion: Both, a stretched spring and a compressed spring have potential energy. Reason: Work is done against the restoring force in each case. (A) 1 (B) 2 (C) 3 (D) 4

Short Answer

Expert verified
The correct answer is (A) 1, as both the Assertion and the Reason are true, and the Reason is the correct explanation for the Assertion.

Step by step solution

01

Understanding the Assertion

: A stretched spring and a compressed spring both have potential energy because they have the capacity to do work when allowed to return to their equilibrium positions. The potential energy stored in the spring is given by the formula: \(PE = \frac{1}{2}kx^2\), where \(PE\) is the potential energy, \(k\) is the spring constant, and \(x\) is the displacement from the equilibrium position. Since the formula does not differentiate between stretched or compressed springs (positive or negative displacement from equilibrium), we can conclude that the Assertion is true.
02

Understanding the Reason

: The restoring force that a spring exerts is proportional to its displacement from the equilibrium position and acts in the opposite direction of the displacement (according to Hooke's Law: \(F = -kx\)). When we stretch or compress a spring, we perform work against this restoring force to increase the spring's potential energy. This means that we are transferring energy from our muscles to the spring in the form of potential energy, and the spring can later release this energy when returning to its equilibrium position. Thus, we can conclude that the Reason is also true.
03

Comparing the Assertion and Reason

: Now that we have established the truth of both the Assertion and the Reason, we can evaluate whether the Reason is indeed the correct explanation for the Assertion. The Assertion states that both a stretched and a compressed spring have potential energy, and the Reason provides an explanation involving the work done against the restoring force when stretching or compressing a spring. This explanation is consistent with the Assertion and directly supports it. Therefore, the Reason is the correct explanation for the Assertion. Since both the Assertion and the Reason are true, and the Reason is the correct explanation for the Assertion, the correct answer is (A) 1.

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Most popular questions from this chapter

A bullet of mass \(\mathrm{m}\) moving with velocity \(\mathrm{v}\) strikes a block of mass \(\mathrm{M}\) at rest and gets embedded into it. The kinetic energy of the composite block will be (A) \((1 / 2) \mathrm{mv}^{2} \times[\mathrm{M} /(\mathrm{m}+\mathrm{m})]\) (B) \((1 / 2) \mathrm{mv}^{2} \times[(\mathrm{m}+\mathrm{m}) / \mathrm{M}]\) (C) \((1 / 2) \mathrm{MV}^{2} \times[\mathrm{m} /(\mathrm{m}+\mathrm{M})]\) (D) \((1 / 2) \mathrm{mv}^{2} \times[\mathrm{m} /(\mathrm{m}+\mathrm{M})]\)

A particle is acted upon by a force \(\mathrm{F}\) which varies with position \(\mathrm{x}\) as shown in figure. If the particle at \(\mathrm{x}=0\) has kinetic energy of \(20 \mathrm{~J}\). Then the calculate the kinetic energy of the particle at \(\mathrm{x}=16 \mathrm{~cm}\). (A) \(45 \mathrm{~J}\) (B) \(30 \mathrm{~J}\) (C) \(70 \mathrm{~J}\) (D) \(135 \mathrm{~J}\)

Bansi does a given amount of work in \(30 \mathrm{sec}\). Jaimeen does the same amount of work .. in \(15 \mathrm{sec}\). The ratio of the output power of Bansi to the Jaimeen is.... (A) \(1: 1\) (B) \(1: 2\) (C) \(2: 1\) (D) \(5: 3\)

A body of mass \(\mathrm{m}\) is accelerated uniformly from rest to a speed \(\mathrm{v}\) in time \(\mathrm{T}\). The instantaneous power delivered to the body in terms of time is given by..... (A) $\left[\left\\{\mathrm{mv}^{2}\right\\} /\left\\{\mathrm{T}^{2}\right\\}\right] \cdot \mathrm{t}$ (B) $\left[\left\\{\mathrm{mv}^{2}\right\\} /\left\\{\mathrm{T}^{2}\right\\}\right] \cdot \mathrm{t}^{2}$ (C) $\left[\left\\{\mathrm{mv}^{2}\right\\} /\\{2 \mathrm{~T}\\}\right] \cdot \mathrm{t}$ (D) $\left[\left\\{\mathrm{mv}^{2}\right\\} /\left\\{2 \mathrm{~T}^{2}\right\\}\right] \cdot \mathrm{t}^{2}$

A body having a mass of \(0.5 \mathrm{~kg}\) slips along the wall of a semispherical smooth surface of radius \(20 \mathrm{~cm}\) shown in figure. What is the velocity of body at the bottom of the surface $?\left(\mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ (A) \(2 \mathrm{~m} / \mathrm{s}\) (B) \(2 \mathrm{~m} / \mathrm{s}\) (C) \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\) (D) \(4 \mathrm{~m} / \mathrm{s}\)
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