Question

Two balls of equal masses m each undergo oblique collision. If collision is perfectly elastic, then angle between their velocities after collision is

(1)π/4

(2)π/3

(3)π/6

(4)π/2

Answer with explanation please!!

Answer 1

Angle between their velocities after collision will be π/2. They will move perpendicular to each other after collision.

Answer 2

Answer:

4] π/2

Explanation:

• By applying conservation of linear momentum

for horizontal direction:

initial momentum = final momentum

mu+0 = mv1cosθ1 + mv2cosθ2.................[1]

for vertical directon:

0 = mv2sinθ1 - mv2sinθ2..................[2]

• collision is perfectly elastic therefore kinetic energy will be conserved

1/2mu² = 1/2mv₁² + 1/2mv₂²

u²= v₁²+v₂²............[3]

Squaring and adding (1) and (2) we get

u² = v₁²+v₂²+2v₁v₂[cosθ₁cosθ₂-sinθ₁sin₂θ]

            or

u² = v₁²+v₂²+2v₁v₂cos[θ₁+θ₂]...........[4]

From equation (3) and (4), we get

2v₁v₂cos[θ₁+θ₂] = 0

cos[θ₁+θ₂] = 0 or θ₁+θ₂= π/2 or 90°

therefore the correct answer is option [4]