KCET2021PhysicsCenter of Mass, Momentum and Collision
A 1 ~kg ball moving at 12 ~ms ⁻¹ collides with a 2 ~kg ball moving in opposite direction at 24 ~ms ⁻¹ . If the coefficient of restitution is 2 / 3 , then their velocities after the collision are
Options
- A-4 ~ms ⁻¹,-28 ~ms ⁻¹
- B-28 ~ms ⁻¹,-4 ~ms ⁻¹
- C4 ~ms ⁻¹, 28 ~ms ⁻¹
- D28 ~ms ⁻¹, 4 ~ms ⁻¹
Correct answer
B. -28 ~ms ⁻¹,-4 ~ms ⁻¹
Step-by-step solution
Given, m₁=1 ~kg aligned &u₁=12 ~ms ⁻¹ &m₂=2 ~kg &u₂=-24 ~ms ⁻¹ aligned (-ve sign implies that, it is travelling in the opposite direction) e= 2 3 As we know, coefficient of restitution, e= v₂-v₁ u₁-u₂ . aligned & 2 3 = v₂-v₁ 12+24 & 2 3 = v₂-v₁ 36 aligned or v₂-v₁=24...(i) According to the law of conservation of momentum, Initial momentum of the system = Final momentum of the system m₁ u₁+m₂ u₂=m₁ v₁+m₂ v₂ Substituting the given values in the above relation, we get array ll & 1 12+2 (-24)=1 v₁+2 v₂ & 12-48=v₁+2 v₂