Question

After a perfectly inelastic collision between two identical particles moving with the same speed in different directions, the speed of the particles becomes half the initial speed. The angle between the velocities of the particles before the collision is

• A. $60^\circ $
• B. $45^\circ $
• C. $120^\circ $
• D. $30^\circ $

Answer 1

Answer: (C)

In a perfectly inelastic collision between two particles, linear momentum is conserved.
Let $\theta$ be the angle between the velocities of the two particles before the collision.
Then $p^{2}=p_{1}^{2}+p_{2}^{2}+2 p_{1} p_{2} \cos \theta$
or $\left(2 m \frac{v}{2}\right)^{2}=(m v)^{2}+(m v)^{2}+2(m v)(m v) \cos \theta$
or $1=1+1+2 \cos \theta$
or $\cos \theta=-\frac{1}{2}$ or $\theta=120^{\circ}$