Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body ' P ' having mass M moving with speed ' $u$ ' has head - on collision elastically with another body ' Q ' having mass ' $m$ ' initially at rest. If $m \ll M$, Body ' Q ' will have a maximum speed equal to'2u' after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:

(C) Both $\mathbf{A}$ and $\mathbf{R}$ are correct and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$.

(A) $\mathbf{A}$ is correct but $\mathbf{R}$ is not correct.

(B) $\mathbf{A}$ is not correct but $\mathbf{R}$ is correct.

(D) Both $\mathbf{A}$ and $\mathbf{R}$ correct but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$.

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Conservation of Momentum

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Body ' P ' having mass M moving with speed '

u

' has head - on collision elastically with another body ' Q ' having mass '

m

' initially at rest. If

m ≪ M

, Body ' Q ' will have a maximum speed equal to'2u' after collision.
Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:

(A) $A$ is correct but $R$ is not correct.
(B) $A$ is not correct but $R$ is correct.
(C)Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$ .✓ Correct
(D)Both $A$ and $R$ correct but $R$ is NOT the correct explanation of $A$ .

Answer: (C)

Solution

For an elastic collision, both momentum and kinetic energy are conserved (Reason R is correct). For a heavy body M colliding with a light body m at rest (

m ≪ M

), the velocity of the light body after collision is given by

v_{m} = \frac{2 M}{M + m} u

. When

m ≪ M

\frac{2 M}{M + m} \approx 2

, so

v_{m} \approx 2 u

(Assertion A is correct). Since the conservation laws directly explain why body Q attains speed 2u, R is the correct explanation of A.

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Single correct option

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JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Conservation of Momentum

Solution

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