Question

A ball A collides elastically with an another identical ball B with velocity 10 m/s at an angle of ${30}^0$ from the line joining their centres $c_{1}and{c}_2.$ select the correct alternative(S):

• A. Velocity of ball B after collision is 5 m/s
• B. Velocity of ball B after collision is $10\sqrt{3}m/s$
• C. Both the balls move at right angles after collision
• D. Kinetic energy will not be conserved here, because collision is not head on.

Answer 1

The correct option is B Velocity of ball B after collision is $10\sqrt{3}m/s$

Since there is no external force,

Momentum is conserved in both sides.

$\Rightarrow u_{1}x=10m/s;u_{2}x=0v_{1}x=v_1\cos 30°;v_{2}x=v_2\cos 30°m{u}_{1}x=m{v}_{2}x+m{v}_{1}x10=v_1\frac{\sqrt{3}}{2}+v_2\frac{\sqrt{3}}{2}\frac{20}{\sqrt{3}}=v_1+v_{2}Now,m{v}_1\sin 30°-m{v}_2\sin 30°=0(v_1-v_2)=0(v_1=v_2)\therefore \frac{20}{\sqrt{3}}=2vv=\frac{10}{\sqrt{3}}\therefore velocity=\frac{10}{\sqrt{3}}$