An object of mass 3m splits into three equal fragments. Two fragments have velocities `vhatj` and `v hati`. The velocity of the third fragment is

Options

A. `v(j-i)`
B. `v(i-j)`
C. `-v(i+j)`
D. `(v(i+j))/sqrt(2)`

Answer

C

Explanation

Initial momentum of 3m mass = 0..................(i)
Due to explosion, this mass splits into three fragmentts of equal masses.

Final momentum of system = (mv + `mvhat(i) + mvhat(j)` ................(ii)
From law of conservation of linear momentum
mv + `mvhat(i) + mvhat(j) = 0`
`rArr v=-v(hat(i)+hat(j))`