A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass and of coefficient of restitution (e). The ratio of velocities of the two spheres, after collision, will be 

Options

A. `e/((e + 1))`
B. `((1 - e)/(1 + e))`
C. `1/e`
D. `((e + 1)/(e ))`

Answer

B

Explanation

Here, `m_1 = m_ = m, u_1 = u , u_2 = 0`
Let `v_1, v_2` be their velocities after collision.
According to principle of conservation of linear momentum
`m u + 0 = m (v_1 + v_2) " or " v_1 + v_2 = u " "….(i)`
by defination , `e = (v_2 - v_1)/(u - 0) " or " v_2 - v_1 = eu " ".....(ii)`
Adding (i) and (ii) , we get, `v_2 = (u(1 + e))/(2)`
Subtracting (ii) from (i), we get, `v_1 = ((1 - e)u)/(2) :. (v_1)/(v_2) = (1 - e)/(1 + e)`.