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. the impulse is `+- m (5 hat(i) + hat(j))`
B. the velocity of the M is `(1/13)(5hat(i) + hat(j))`
C. Both (a) and (b) are wrong
D. Both (a) and (b) are correct

Answer

D

Explanation

`m(hat(i) + 2hat(j)) = m(-2hat(i) + hat(j)) + Mv` (Put M = 12m)`
`therefore v= (5hat(i) + hat(j))/13`
`J_(m) = p_(f) - p_(i)` of m
`=[(-2hat(i)+hat(j))-(3hat(i) + 2hat(j))]`
`therefore J_(m) = m(5hat(i) + hat(j)`