A ball , moving with a speed of `10 sqrt(3) m//s` , strikes an identical stationary ball such that after the collision , the direction of each ball makes an angle of `30^(@)`with the original line of motion. The speeds of two balla after the collision are , respectively.

Options

A. `5 m//s , 10 m//s`
B. `10 m//s , 5 m//s`
C. `5 m//s , 5 m//s`
D. `10 m//s , 10 m//s`

Answer

D

Explanation

Momentum conservation:
`x : m xx 10 sqrt(3) = mv_(1) cos 30^(@) + mv_(2) cos 30^(@)` (i)
`y : 0 = mv_(1) sin 30^(@) - mv_(2) sin 30^(@) rArr v_(1) = v_(2)` (ii)
From (i) and (ii) , we get
`10 sqrt(3) = 2v_(1) cos 30^(@) = 2v_(1) xx (sqrt(3))/(2) rArr v_(1) = 10 m//s`