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

A ball having a mass of 0.50 kg and travelling at a speed of 5.0 m/s collides with another ball of mass 1.0 kg . Following the collision, the two stick together and stay motionless. Determine the velocity of the 1.0 kg block prior to the collision.

Options

  1. A2.5 m/s opposite to the direction of motion of the first ball
  2. B1.25 m/s opposite to the direction of motion of the first ball
  3. C5.0 m/s opposite to the direction of motion of the first ball
  4. D2.5 m/s in the direction of motion of the first ball

Correct answer

A. 2.5 m/s opposite to the direction of motion of the first ball

Step-by-step solution

According to the law of conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision. m₁ v₁ + m₂ v₂ = (m₁ + m₂) v_f Given m₁ = 0.50 kg , v₁ = 5.0 m/s , m₂ = 1.0 kg , and v_f = 0 . Substituting the values: 0.50 5.0 + 1.0 v₂ = (0.50 + 1.0) 0 2.5 + v₂ = 0 v₂ = -2.5 m/s The negative sign indicates that the velocity of the second ball is opposite to the direction of motion of the first ball.

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