Question

After perfectly inelastic collision between two identical particles, moving with the same initial speed in different directions, the speed of the composite particle becomes half the initial speed of an individual particle. Find the angle made by velocity of both the particles with $x-$axis before collision.

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${75}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

As the total momentum of the system remains conserved, the magnitude of total momentum of the system before and after collision, must be equal.

$i.e.p^2=p_1^2+p_2^2+2p_1{p}_2\cos 2\alpha$

$\Rightarrow \left[2m\right(v/2){]}^2=(mv{)}^2+(mv{)}^2+2(mv\left)\right(mv)\cos 2\alpha$

$\Rightarrow \cos 2\alpha =-\frac{1}{2}$

$\Rightarrow 2\alpha ={120}^{\circ }$

$\Rightarrow \alpha ={60}^{\circ }$

Hence, option $\left(B\right)$ is the correct answer.