Q 11-05-161JEE MainJEE Main 2020 (6 Sep, Shift 1)Medium
Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is ______.
Numerical value type. Enter your answer.
Answer: 120
Let each mass be $m$, each speed $v$, and $\theta$ the angle between the velocities. The magnitude of the total momentum is $2mv\cos(\theta/2)$.
After sticking together: $2m\cdot\dfrac v2 = mv$.
$$2mv\cos\frac\theta2 = mv \Rightarrow \cos\frac\theta2 = \frac12 \Rightarrow \theta = 120^\circ$$
Solution by Sreeraj P, M.Sc Physics