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Chapter 4: Problem 522

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: In the elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason: In the elastic collision the linear momentum of the system is conserved. (A)1 (B) 2 (C) 3 (D) 4

Short Answer

Expert verified
Based on the analysis, both the assertion and the reason are true, and the reason is indeed the correct explanation for the assertion. Therefore, the correct answer is (A) 1.

Step by step solution

01

Analyze the assertion

We are given that in an elastic collision between two bodies, the relative speed of the bodies after the collision is equal to the relative speed before the collision. This is a property of elastic collisions and we recall that in an elastic collision, both linear momentum and kinetic energy are conserved.
02

Analyze the reason

The given reason states that in an elastic collision, the linear momentum of the system is conserved. This is a fundamental principle in physics called the conservation of linear momentum. For elastic collisions, not only linear momentum is conserved, but also the kinetic energy of the system.
03

Compare assertion and reason

Since both the assertion and reason are true statements regarding elastic collisions and linear momentum conservation, we now have to determine if the reason provided is the correct explanation for the assertion. In elastic collisions, due to both linear momentum and kinetic energy being conserved, it is possible to show mathematically that the relative speed of the objects after the collision is equal to the relative speed before the collision. The conservation of linear momentum is an important part of proving this. Therefore, the reason given is indeed the correct explanation for the assertion.
04

Choose the correct option

Based on our analysis in the previous steps, both the assertion and reason are true, and the reason is the correct explanation for the assertion. Therefore, the correct option is: (A) 1

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Most popular questions from this chapter

A force \(\mathrm{F}=\mathrm{kx}\) (where \(\mathrm{k}\) is positive constant) is acting on a particle. Match column-I and column-II, regarding work done in displacing the particle. $$ \begin{array}{|l|l|} \hline \text { Column - i } & \text { Column - ii } \\ \hline \text { (a) From } \mathrm{x}=-4 \text { to } \mathrm{x}=-2 & \text { (P) Positive } \\ \hline \text { (b) From } \mathrm{x}=-2 \text { to } \mathrm{x}=-4 & \text { (Q) zero } \\ \hline \text { (c) From } \mathrm{x}=-2 \text { to } \mathrm{x}=+2 & \text { (R) negative } \\ \hline \end{array} $$ (A) \(\mathrm{a}-\mathrm{R}, \mathrm{b}-\mathrm{P}, \mathrm{c}-\mathrm{Q}\) (B) \(a-P, b-Q, c-R\) (C) \(a-R, b-Q, c-P\) (D) \(\mathrm{a}-\mathrm{Q}, \mathrm{b}-\mathrm{P}, \mathrm{c}-\mathrm{R}\)

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 spring of spring constant \(10^{3} \mathrm{~N} / \mathrm{m}\) is stretched initially \(4 \mathrm{~cm}\) from the unscratched position. How much the work required to stretched it further by another \(5 \mathrm{~cm}\) ? (A) \(6.5 \mathrm{NM}\) (B) \(2.5 \mathrm{NM}\) (C) \(3.25 \mathrm{NM}\) (D) \(6.75 \mathrm{NM}\)

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: Work done by centripetal force is zero. Reason: This is because centripetal force is always along the tangent. (A)1 (B) 2 (C) 3 (D) 4

A body initially at rest undergoes one dimensional motion with constant acceleration. The power delivered to it at time \(\mathrm{t}\) is proportional to..... (A) \(\mathrm{t}^{1 / 2}\) (B) \(t\) (C) \(\mathrm{t}^{3 / 2}\) (D) \(\mathrm{t}^{2}\)
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