A ball moving with a velocity of 6 m/s strikes an identical stationary ball. After collision each ball moves at angle of `30^@` with the original line of motion. Assuming that the collision is elastic, what are the speeds of the balls after the collision?   

Options

A. `(sqrt3)/2 m//s, 2sqrt(3) m//s`
B. `3 m//s, 2sqrt(3) m//s`
C. `2sqrt(3) m//s, 2sqrt(3) m//s`
D. `sqrt(3) m/s, sqrt(3) m//s`

Answer

C

Explanation

According to the law of conservation of momentum along vertical and horizontal directions, we get
`0 = mv_1 sin 30^@ - m v_2 sin 30^@ `
or `v_1 = v_2 " " …..(i)`
`m xx u + m xx 0 = mv_1 cos 30^@ + mv_2 cos 30^@ " " .......(ii)`
Putting eqn. (i) in eqn. (ii), we get , `m u = 2 mv_1 cos 30^@`
or `m xx 6 = 2 xx m xx v_1 xx (sqrt3)/(2) " or " v_1 = (6)/(sqrt3) = 2sqrt(3) m//s`
From (i), we get, `v_1 = 2sqrt(3) m//s`.