A particle of mass 2 kg moving with a speed of 6 m/s collides elastically with another particle of mass 4 kg traveling in same direction with a speed of 2 m/s . The maximum possible deflection of the 2 kg particle is

Question

A particle of mass 2 kg moving with a speed of 6 m/s collides elastically with another particle of mass 4 kg traveling in same direction with a speed of 2 m/s . The maximum possible deflection of the 2 kg particle is, 37 0, 45 0, 53 0, 60 0

MARKS App · Accepted Answer

Let situations after collision for balls are According to question 2 v 1 + 4 v 3 = 20 2 v 2 = 4 v 4 1 2 × 2 v 1 2 + v 2 2 + 1 2 × 4 v 3 2 + v 4 2 = 1 2 × 2 × 6 2 + 1 2 × 4 × 2 2 = 44 i.e. v 1 2 + v 2 2 + 2 v 3 2 + v 2 2 2 = 44 i.e. v 1 2 + 3 2 v 2 2 + 10 - v 1 2 2 2 = 44 i.e. 2 v 1 2 + 3 v 2 2 + 100 - 20 v 1 + v 1 2 = 88 i.e. 3 v 1 2 + 3 v 2 2 - 20 v 1 + 12 = 0 i.e. 12 v 1 2 - 20 v 1 + 3 v 2 2 v 1 2 + 3 = 0 Quadratic in 1 v 1 which is real ∴ D ≥ 0 ∴ - 20 2 - 4 × 12 1 + v 2 2 v 1 2 × 3 ≥ 0 ∴ 1 + v 2 2 v 1 2 ≤ 400 144 v 2 2 v 1 2 ≤ 256 144 - 16 12 ≤ v 2 v 1 ≤ 16 12 ⇒ k = tan ⁡ θ ≤ 4 3 ⇒ θ ≤ 53 o

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