A partical of mass `'m'` moving with a velocity `(3 hat(i)+2hat(j))m//s` collides with statinary mass `'M'` and finally `'m'` moves with a velocity `(-2hat(i)+hat(j))m//s` if `(m)/(M) = (1)/(13)` the velocity of the `M` after collision is?

Options

A. `(5 hat(i)+hat(j))m//s`
B. `(5 hat(i)-hat(j))m//s`
C. `((5 hat(i))/(13)-(hat(j))/(13))m//s`
D. `((5 hat(i))/(13)+(hat(j))/(13))m//s`

Answer

D

Explanation

Applying law of conservation of momentum
`m = (3hat(i)+2hat(j)) + 0 = m (-2 hat(i)+hat(j))+MV`
`m(3hat(i)+2hat(j)+2hat(i)-hat(j)) = Mv, v = (m)/(M)(5hat(i)+hat(j))`
`v = (1)/(13)(5hat(i)+hat(j))`