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NEETPhysicsCenter of Mass, Momentum and Collision

An object moving in a two-dimensional plane with an initial velocity (- i + 4 j ) m/s explodes into two fragments. Immediately after the explosion, the velocity of the first fragment is (5 i - 2 j ) m/s and the velocity of the second fragment is (-5 i + 8 j ) m/s . The ratio of the mass of the first fragment to the mass of the second fragment is

Options

  1. A2:3
  2. B3:2
  3. C1:5
  4. D2:5

Correct answer

A. 2:3

Step-by-step solution

Let the masses of the two fragments be m₁ and m₂ . According to the law of conservation of linear momentum, the total momentum before the explosion is equal to the total momentum after the explosion: (m₁ + m₂) v = m₁ v ₁ + m₂ v ₂ Substituting the given velocity vectors: (m₁ + m₂)(- i + 4 j ) = m₁(5 i - 2 j ) + m₂(-5 i + 8 j ) Equating the i components on both sides: -(m₁ + m₂) = 5m₁ - 5m₂ -m₁ - m₂ = 5m₁ - 5m₂ 4m₂ = 6m₁ m₁ m₂ = 4 6 = 2 3 Equating the j components yields the same result: 4(m₁ + m₂) = -2m₁ + 8m₂ 4m₁ +

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