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AP EAMCET202119 Aug 2021Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A particle of mass ' m ' , moving with a velocity ' v ' makes an elastic collision in one dimension with a stationary particle of mass ' m ' . During the collision, they remain in contact with each other for an extremely small time ' T ' : Their force of contact, with time is shown in the figure. Then F 0 =

Options

  1. A2 m v T
  2. B4 m v 3 T
  3. Cm v T
  4. D3 m v 4 T

Correct answer

B. 4 m v 3 T

Step-by-step solution

In an elastic head-on collision between two particles, the velocity of the particle gets exchanged, therefore net change of momentum of a particle is, ∆ p = m ∆ v = m v - 0 = m v From newton's second law, the rate of change of momentum is force. F = d p d t ⇒ F d t = d p ⇒ F T = ∆ p Here, F   is force of contact during the collision for a small-time T   that causes the ∆ p   change in momentum of particle. Thus, the area under the graph of F - t   curve gi

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