JEE Main 202127 JulyMorning Shift

Exam: JEE Main
Year: 2021
Date: 27 July
Shift: Morning Shift
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Main 2021 · 27 July · Morning Shift · Physics · Center of Mass, Momentum and Collision

Three objects A, B and C are kept in a straight line on a...

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A, B$ and $C$ are $m, 2m$ and $2m$ respectively. $A$ moves towards $B$ with a speed of $9m{s}^{- 1}$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C .$ All motions occur along the same straight line. The final speed of $C$ is :

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are

Options

A $6m{s}^{- 1}$
B $9m{s}^{- 1}$
C $4m{s}^{- 1}$
D $3m{s}^{- 1}$

Correct answer

D. $3m{s}^{- 1}$

Step-by-step solution

Collision between $A$ and $B$

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are

$m \times 9 = m{v}_{1} + 2m{v}_{2}$ (from momentum conservation)
$e = 1 = \dfrac{{v}_{2} - {v}_{1}}{9}$
$⇒ {v}_{2} = 6m{sec}^{- 1}, {v}_{1} = - 3m{sec}^{- 1}$
Collision between $B$ and $C$

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are

$2m \times 6 = 4mv$ (from momentum conservation)
$v = 3m{s}^{- 1}$

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