A steel ball of radius 2 ~cm is at rest on a frictionless surface. Another steel ball of radius 4 ~cm moving with velocity of 81 cms ⁻¹ collides elastically with the ball which is at rest. After collision the ball with radius of 2 ~cm moves with speed of

Step-by-step solution

Radius of first steel ball, r₁=2 ~cm =2 10⁻² ~m Radius of second steel ball, r₂=4 ~cm =4 10⁻² ~m Mass of first steel ball, m₁=V₁ = 4 3 r₁^3 [ = density ] Similarly, m₂= 4 3 r₂^3 m₁ m₂ = r₁^3 r₂^3 = (2 10⁻² )^3 (4 10⁻² )^3 = 1 8 m₂=8 m₁ For elastic collision, velocity of first ball, v₁= ( m₁-m₂ m₁+m₂ ) u₁+ ( 2 m₂ m₁+m₂ ) u₂ Here, u₁=0 and u₂=81 cms ⁻¹ aligned v₁ & = ( m₁-m₂ m₁+m₂ ) 0+ ( 2 m₂ m₁+m₂ ) 81 & =0+ 2 8 m₁ m₁+8 m₁ 81 [from Eq. (i)] & = 16 9 81=144 ~cm ~s ⁻¹ aligned [from Eq. (i)]