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JEE Main 20202 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
2 September
Shift
Morning Shift
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

JEE Main 2020 · 2 September · Morning Shift · Physics · Center of Mass, Momentum and Collision

A particle of mass m with an initial velocity u ^ i collides...

A particle of mass mm with an initial velocity u\overset{^}{i} collides perfectly elastically with a mass 3m3m at rest. It moves with a velocity v\overset{^}{j} after collision, then, vv is given by

Options

  1. Av=23uv = \sqrt{\dfrac{2}{3}}u
  2. Bv=u3v = \dfrac{u}{\sqrt{3}}
  3. Cv=u2v = \dfrac{u}{\sqrt{2}}
  4. Dv=16uv = \dfrac{1}{\sqrt{6}}u

Correct answer

C. v=u2v = \dfrac{u}{\sqrt{2}}

Step-by-step solution

From momentum conservation

mu\overset{^}{i} + 0 = mv\overset{^}{j} + 3m\overset{\to}{v} '

\overset{\to}{v} ' = \dfrac{u}{3}\overset{^}{i} - \dfrac{v}{3}\overset{^}{j}

From kinetic energy conservation 12mu2=12mv2+12(3m)((u3)2+(v3)2)\dfrac{1}{2}m{u}^{2} = \dfrac{1}{2}m{v}^{2} + \dfrac{1}{2} ( 3m ) \left({\left(\dfrac{u}{3}\right)}^{2} + {\left(\dfrac{v}{3}\right)}^{2}\right)

solving v=u2v = \dfrac{u}{\sqrt{2}}

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