Question

Ball A of mass m moving with velocity V collides head on with a stationary ball B of mass m. If e be the coefficient of restitution, then which of the following statements are correct ?

• A. The ratio of velocities of balls A and B after the collision is $\left(\frac{1+e}{1-e}\right)$
  
• B. The ratio of the final and initial velocities of ball A is $\left(\frac{1-e}{2}\right)$
  
• C. The ratio of the velocities of balls A and B after the collision is $\left(\frac{1-e}{1+e}\right)$
  
• D. The ratio of the final and initial velocities of ball B is $\left(\frac{1+e}{2}\right)$

Answer 1

Answer: (B), (C)

The correct options are
B The ratio of the final and initial velocities of ball A is $\left(\frac{1-e}{2}\right)$

C The ratio of the velocities of balls A and B after the collision is $\left(\frac{1-e}{1+e}\right)$



$e=\frac{V_2-V_1}{V}mV=m{V}_1+m{V}_2{V}_2=\frac{(1+e)V}{2}{V}_1=\frac{(1-e)V}{2}$