A small smooth disc of mass `m` and radius moving with an initial velocity `'v'` along the positive `x-` axis collided with a big disc of mass `2m` and radius `2r` which was initially at rest with its centre at origin as shown in figure.

If the coefficient of restitution is `0` then velocity of largen disc after collision is

Options

A. `(8v)/(27)hat(i) -(2sqrt(2))/(27)vhat(j)`
B. `(8v)/(27)hat(i) +(2sqrt(2))/(27)vhat(j)`
C. `(v)/(3)hat(i)`
D. `(2sqrt(2))/(27)vhat(i)-(8v)/(2)hat(j)`

Answer

A

Explanation

The larger sphere will move along line of impact.
`Abe=0,` velocity of larger sphere .
`v'=(mvcos theta )/(m+2m)=(v cos theta )/(3)`
velocity of larger sphere
`=v'cos theta hat(i)-v' sin theta hat(j)`
`=(v)/(3) cos^(2)theta hat(i)-(v)/(3) sin theta cos theta hat(j)`
`=(8)/(27)hat(i)-(2sqrt(2))/(27)hat(j)`