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Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision

A bullet of mass m travelling at a speed v strikes a ball of mass M that is initially at rest. A small part with mass m' breaks off from the ball and sticks to the bullet. The remaining ball is observed to travel at a speed v₁ in the bullet's direction. Determine the velocity of the bullet following the collision.

Options

  1. Amv - Mv₁ m + m' in the initial direction
  2. Bmv - (M - m')v₁ m + m' in the initial direction
  3. Cmv + (M - m')v₁ m + m' in the initial direction
  4. Dmv - (M - m')v₁ m in the initial direction

Correct answer

B. mv - (M - m')v₁ m + m' in the initial direction

Step-by-step solution

By the principle of conservation of linear momentum, the total initial momentum of the system is equal to the total final momentum. Initial momentum of the system is p_i = mv + M(0) = mv . After the collision, a part of mass m' breaks off from the ball and sticks to the bullet. The new mass of the bullet becomes m + m' . Let its final velocity be v₂ . The remaining mass of the ball is M - m' , and it moves with a velocity v₁ in the initial direction of the bullet. Final momentum of the system is p_f = (m + m')v₂ +

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