A smooth ball `'A'` moving with velocity `'V'` collides with another smooth identical ball at rest. After collision both the balls move with same speed with angle between their velocities `60^(@)`. No external force acts on the system of balls.

The value of coefficient of resititution is

Options

A. 1
B. `(1)/(3)`
C. `(1)/(sqrt(3))`
D. 0

Answer

B

Explanation

From conservation of momentum
`mv=mv' cos 30^(@)+mv' cos 30^(@)`
`:. V' =(v)/(2 cos 30^(@))=(v)/(sqrt(3))`
Initially `B` was at rest, therefore line of impact is along final velcoity of `B`.
`:. e=(v'-v'cos 60^(@))/(v cos 30)=((1)/(2)(v)/(sqrt(3)))/(vxx(sqrt(3))/(2))=(1)/(3)`