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Chapter 4: Problem 529

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: stopping distance \(=[\\{\) Kinetic energy \(\\} /\\{\) Stopping force \(\\}]\) Reason: Work done in stopping a body is equal to K.E. of the body. (A) 1 (B) 2 (C) 3 (D) 4

Short Answer

Expert verified
(A) 1

Step by step solution

01

Understand the Assertion

The Assertion states that the stopping distance is equal to the kinetic energy divided by the stopping force. Stopping distance is the distance required for an object to come to a complete stop. In general, the stopping distance depends on several factors such as the initial speed, the mass of the object, and the stopping force. The most common formula for stopping distance is given by: \(d = \frac{v^2}{2a}\) where: \(d\) = stopping distance, \(v\) = initial velocity, \(a\) = deceleration or stopping force/mass. Now, since kinetic energy is given by the formula: K.E. = \(\frac{1}{2}mv^2\) We need to check if the stopping distance can be represented as the kinetic energy divided by the stopping force.
02

Understand the Reason

The Reason states that the work done in stopping a body is equal to its kinetic energy. According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. W = ΔK.E. Since the final kinetic energy of a stopped object is 0, we can say that the work done in stopping a body is equal to its initial kinetic energy: W = K.E. As we know that work done (W) is also given by the formula: W = F × d Where F is the stopping force and d is the distance.
03

Determine the relationship between Assertion and Reason

Now, let's relate the stopping distance formula with the work-energy theorem. From the work-energy theorem, we have: \(W = F \times d = K.E.\) We can express the stopping distance as: \(d = \frac{K.E.}{F}\) The stopping distance formula derived here matches with the Assertion. This demonstrates that the Assertion is true. Additionally, the Reason (work done in stopping a body is equal to its kinetic energy) is also true and provides the correct explanation for this Assertion.
04

Choose the correct answer

Since both the Assertion and Reason are true, and the Reason provides the correct explanation for the Assertion, the correct answer is (A) 1.

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Most popular questions from this chapter

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 uniform chain of length \(2 \mathrm{~m}\) is kept on a table such that a length of \(50 \mathrm{~cm}\) hangs freely from the edge of the table. The total mass of the chain is \(5 \mathrm{~kg}\). What is the work done in pulling the entire chain on the table. $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{2}\right)$ (A) \(7.2 \mathrm{~J}\) (B) \(3 \mathrm{~J}\) (C) \(4.6 \mathrm{~J}\) (D) \(120 \mathrm{~J}\)

The potential energy of a body is given by \(\mathrm{U}=\mathrm{A}-\mathrm{Bx}^{2}\) (where \(\mathrm{x}\) is displacement). The magnitude of force acting on the particle is (A) constant (B) proportional to \(\mathrm{x}\) (C) proportional to \(\mathrm{x}^{2}\) (D) Inversely proportional to \(\mathrm{x}\)

A body of mass \(6 \mathrm{~kg}\) is under a force, which causes a displacement in it given by $\mathrm{S}=\left[\left(2 \mathrm{t}^{3}\right) / 3\right](\mathrm{in} \mathrm{m}) .$ Find the work done by the force in first one seconds. (A) \(2 \mathrm{~J}\) (B) \(3.8 \mathrm{~J}\) (C) \(5.2 \mathrm{~J}\) (D) \(24 \mathrm{~J}\)

The bob of simple pendulum (mass \(\mathrm{m}\) and length 1 ) dropped from a horizontal position strike a block of the same mass elastically placed on a horizontal frictionless table. The K.E. of the block will be (A) \(2 \mathrm{mg} 1\) (B) \(\mathrm{mg} 1 / 2\) (C) \(\mathrm{mg} 1\) (D) zero
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