A steel ball of radius `2 cm` is at rest on a frictionless surface. Another ball of radius `4 cm` moving at a velocity of `81 cm//see` collides elast cally with first ball. After collision the smaller ball moves with speed of

Options

A. `81 cm//s`
B. `63 cm//s`
C. `144 cm//s`
D. None of these

Answer

C

Explanation

Mass `prop` volume
`m_(1) prop (4)/(3) pi (2)^(3) , m_(2) prop (4)/(3) pi (4)^(3)`
`m_(1) = m, m_(2) = 8 m`
`8m xx 81 = 8 m v_(1) + mv_(2) rArr 8 v_(1) + v_(2) = 648` (i)
`v_(1) + 81 = v_(2) + 0 rArr v_(1) - v_(2) = - 81` (ii)
`v_(2) = 144 m//s`