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NEETPhysicsCenter of Mass, Momentum and Collision

A block of mass m₁ moving with a velocity v on a smooth horizontal surface collides completely inelastically with another block of mass m₂ which is initially at rest. If the combined system moves with a velocity of v 5 after the collision, what is the ratio of their masses m₁ : m₂ ?

Options

  1. A4:1
  2. B1:4
  3. C1:5
  4. D5:1

Correct answer

B. 1:4

Step-by-step solution

By the principle of conservation of linear momentum, the initial momentum of the system is equal to the final momentum. Initial momentum = m₁ v + m₂(0) = m₁ v Since the collision is completely inelastic, the two blocks stick together and move with a common velocity. Final momentum = (m₁ + m₂) ( v 5 ) Equating initial and final momentum: m₁ v = (m₁ + m₂) ( v 5 ) Cancelling v from both sides and cross-multiplying: 5m₁ = m₁ + m₂ 4m₁ = m₂ m₁ m₂ = 1 4 Thus, the ratio m₁ : m₂ is 1:4 . Answer: 1:4

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