NEETPhysicsCenter of Mass, Momentum and Collision
A moving body of mass M with velocity v₀ i explodes into two fragments of masses m₁ and m₂ . Immediately after the explosion, the fragment of mass m₁ comes to rest. Match the mass ratios given in List-I with the corresponding final velocity of the second fragment given in List-II. List-I List-II (A) 1:1 (I) 1.5 v₀ i (B) 1:2 (II) 2 v₀ i (C) 2:1 (III) 3 v₀ i (D) 3:1 (IV) 4 v₀ i Choose the correct answer from the option
Options
- A(A) - I, (B) - II, (C) - III, (D) - IV
- B(A) - II, (B) - III, (C) - I, (D) - IV
- C(A) - II, (B) - I, (C) - III, (D) - IV
- D(A) - II, (B) - I, (C) - IV, (D) - III
Correct answer
C. (A) - II, (B) - I, (C) - III, (D) - IV
Step-by-step solution
By the principle of conservation of linear momentum, the total initial momentum equals the total final momentum. (m₁ + m₂) v₀ i = m₁ (0) + m₂ v₂ v₂ = m₁ + m₂ m₂ v₀ i = ( m₁ m₂ + 1 ) v₀ i For (A) m₁:m₂ = 1:1 m₁ m₂ = 1 v₂ = (1 + 1) v₀ i = 2 v₀ i (Matches II) For (B) m₁:m₂ = 1:2 m₁ m₂ = 0.5 v₂ = (0.5 + 1) v₀ i = 1.5 v₀ i (Matches I) For (C) m₁:m₂ = 2:1 m₁ m₂ = 2 v₂ = (2 + 1) v₀ i = 3 v₀ i (Matches III) For (D) m₁:m₂ = 3:1 m₁ m₂ = 3 v₂ = (3 + 1) v₀ i = 4 v₀ i (Matches IV) Therefore, the correct matching is (A) - II, (B