After a completely inelastic collision two objects of the same mass and same initial speed are found to move away together at half their initial speed. Find the angle between the initial velocities of the objects.

Options

A. `120^@`
B. `90^@`
C. `180^@`
D. `60^@`

Answer

A

Explanation

Let `theta` be the desired angle. Linear momentum of the system will remain conserved.

Hence, `p^2=p_1^2+p_2^2+2p_2p_2costheta`
or `{2m(v/2)}^2=(mv)^2+(mv)^2+2(mv)(mv)costheta`
or `1=1+1+2costheta` or `costheta=-1/2`
`:. theta=120^@`