Question

In a collinear collision, a particle with an initial speed v₀ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :

(1) √2v₀ 

(2) v₀/2 

(3) v₀/√2 

(4) v₀/4 

Answer 1

Ans. (1)

initial

1/2 mv₁²+1/2 mv₂²= 3/2 (1/2 mv₀²)...(1)
from momentum conservation
mv₀ = m(v₁ + v₂) ...(2)
(v₁ + v₂)² = v₀²

Answer 2

Solution: We have

mv₀ = mv₁ + mv₂ ….(1)
(momentum conservation)
KE_f = KE_i + 0.5 KE_i
KE_f = 1.5 KE_i
m(v₁² + v₂²)/2 = mv₀²/2 × 1.5 ….(2)
From (1) v₁ + v₂ = v₀
From (2) v₁² + v₂² = 1.5 v₂²

Comments

Nice ur ans is simple and helpful keep it up

---

@Pratibha Patra Thanks!