Particle A of mass m _ 1 moving with velocity ( 3 ^ i + ^ j ) ms ^ - 1 collides with another particle B of mass m _ 2 which is at rest initially. Let → v 1 and → v 2 be the velocities of particles A and B after

Correct answer: D. 105 ^ ° m _ 1 → u 1 + m _ 2 → u 2 = m _ 1 → v 1 + m _ 2 → v 2 2 m _ 2 ( 3 ^ i + ^ j ) + m _ 2 × 0 = 2 m _ 2 ( ^ i + 3 ^ j ) + m _ 2 × → v 2 2 3 ^ i + 2 ^ j = 2 ^ i + 2 3 ^ j + → v 2 → v 2 = ( 3 - 1 ) ^ i - ( 3 - 1 ) ^ j → v 1 = ^ i + 3 ^ j Angle between → v 1 and → v 2 is 105 ^ °

JEE Main 20206 SeptemberEvening Shift

Exam: JEE Main
Year: 2020
Date: 6 September
Shift: Evening Shift
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Main 2020 · 6 September · Evening Shift · Physics · Center of Mass, Momentum and Collision

Particle A of mass m _ 1 moving with velocity ( 3 ^ i + ^ j ) ms ^...

Particle

A

of mass

{m}_{1}

moving with velocity \left(\sqrt{3}\overset{^}{i} + \overset{^}{j}\right){ms}^{- 1}

collides with another particle

of mass

{m}_{2}

which is at rest initially. Let

\overset{\to}{v}1

and

\overset{\to}{v}2

be the velocities of particles

A and B

after collision respectively. If

{m}_{1} = 2{m}_{2}

and after collision

\overset{\to}{v}1 - \left(\overset{^}{i} + \sqrt{3}\overset{^}{j}\right){ms}^{- 1}

, the angle between

\overset{\to}{v}1 and \overset{\to}{v}2 is : Particle A of mass m _ 1 moving with velocity ( 3 ^ i + ^ j ) ms ^ - 1 collides with another particle B of mass m _ 2

Options

A ${15}^{°}$
B ${60}^{°}$
C $- {45}^{°}$
D ${105}^{°}$

Correct answer

D. ${105}^{°}$

Step-by-step solution

${m}_{1}\overset{\to}{u}1 + {m}_{2}\overset{\to}{u}2 = {m}_{1}\overset{\to}{v}1 + {m}_{2}\overset{\to}{v}2$

$2{m}_{2} ( \sqrt{3}\overset{^}{i} + \overset{^}{j} ) + {m}_{2} \times 0 = 2{m}_{2} ( \overset{^}{i} + \sqrt{3}\overset{^}{j} ) + {m}_{2} \times \overset{\to}{v}2$

$2\sqrt{3}\overset{^}{i} + 2\overset{^}{j} = 2\overset{^}{i} + 2\sqrt{3}\overset{^}{j} + \overset{\to}{v}2$

$\overset{\to}{v}2 = ( \sqrt{3} - 1 ) \overset{^}{i} - ( \sqrt{3} - 1 ) \overset{^}{j}$

$\overset{\to}{v}1 = \overset{^}{i} + \sqrt{3}\overset{^}{j}$

Angle between $\overset{\to}{v}1$ and $\overset{\to}{v}2$ is ${105}^{°}$

Particle A of mass m _ 1 moving with velocity ( 3 ^ i + ^ j ) ms ^ - 1 collides with another particle B of mass m _ 2

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