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JEE Main 20199 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
9 April
Shift
Evening Shift
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

JEE Main 2019 · 9 April · Evening Shift · Physics · Center of Mass, Momentum and Collision

A particle of mass m is moving with speed 2v and collides with a...

A particle of mass mm is moving with speed 2v2\text{v} and collides with a mass 2m2m moving with speed v\text{v} in the same direction. After the collision, the first mass is stopped completely while the second one splits into two particles each of mass m,m, which move at an angle 45o{45}^{o} with respect to the original direction. The speed of each of the moving particle will beA particle of mass m is moving with speed 2v and collides with a mass 2m moving with speed v in the same direction.A particle of mass m is moving with speed 2v and collides with a mass 2m moving with speed v in the same direction.

Options

  1. A2v\sqrt{2}\text{v}
  2. Bv2\dfrac{\text{v}}{\sqrt{2}}
  3. C22v2\sqrt{2}\text{v}
  4. D\dfrac{\text{v}}{\left(2\sqrt{2}\right)}

Correct answer

C. 22v2\sqrt{2}\text{v}

Step-by-step solution

A particle of mass m is moving with speed 2v and collides with a mass 2m moving with speed v in the same direction. A particle of mass m is moving with speed 2v and collides with a mass 2m moving with speed v in the same direction.

As 2m2m splits into equal parts, v1=v2{v}_{1} = {v}_{2} and θ=450\theta = 4{5}^{0}
From conservation of linear momentum,
m(2v)+2m(v)=2[mv1cos⁡45o]m\left(2v\right) + 2m\left(v\right) = 2\left[m{v}_{1}\cos 4{5}^{o}\right]
⇒v1=v2=22v⇒ {v}_{1} = {v}_{2} = 2\sqrt{2}\text{v}
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