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

As depicted in the figure, two blocks of masses m₁ and m₂ are joined by a spring having spring constant k . The block of mass m₂ is subjected to a sharp impulse such that it gains a velocity v₀ towards the right. Find the velocity of the centre of mass.

Options

  1. A(m₁ + m₂) v₀ m₂
  2. Bm₂ v₀ m₁ + m₂
  3. Cm₁ v₀ m₁ + m₂
  4. Dm₂ v₀ m₁

Correct answer

B. m₂ v₀ m₁ + m₂

Step-by-step solution

Initial velocity of block m₁ , v₁ = 0 . Initial velocity of block m₂ , v₂ = v₀ . The velocity of the centre of mass of the system is given by: v_ cm = m₁ v₁ + m₂ v₂ m₁ + m₂ Substituting the values: v_ cm = m₁(0) + m₂(v₀) m₁ + m₂ v_ cm = m₂ v₀ m₁ + m₂ Since there is no net external force acting on the system in the horizontal direction after the impulse, the velocity of the centre of mass remains constant.

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