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JEE Main 202310 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
10 April
Shift
Morning Shift
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

JEE Main 2023 · 10 April · Morning Shift · Physics · Center of Mass, Momentum and Collision

A particle of mass m moving with velocity v collides with a...

A particle of mass mm moving with velocity vv collides with a stationary particle of mass 2m2m. After collision, they stick together and continue to move together with velocity

Options

  1. Av3\dfrac{v}{3}
  2. Bv4\dfrac{v}{4}
  3. Cvv
  4. Dv2\dfrac{v}{2}

Correct answer

A. v3\dfrac{v}{3}

Step-by-step solution

The law of conservation of momentum is given as

m1u+m2u′=(m1+m2)v′{m}_{1}u + {m}_{2}u ' = \left({m}_{1} + {m}_{2}\right)v '

The given data is

u=vu′=0ms−1m1=mm2=2mu = vu ' = 0m{s}^{- 1}{m}_{1} = m{m}_{2} = 2m

Using the conservation of momentum equation,

mv+2m(0)=(m+2m)v′⇒v′=mv3m=v3mv + 2m ( 0 ) = ( m + 2m ) v ' ⇒ v ' = \dfrac{mv}{3m} = \dfrac{v}{3}

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