Question

A sphere of mass m moving with constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, aid the ratio of velocities of the two spheres after die collision will be

• A. $ \frac{1}{e} $
• B. $ \frac{1-e}{1+e} $
• C. $ \frac{e}{1+e} $
• D. $ \frac{e+1}{e} $

Answer 1

The Correct Option is B

The velocity of sphere of mass $ m={{u}_{1}} $ The velocity of another sphere of mass m $ ={{u}_{2}}=0 $ The velocity after collision of first sphere $ {{v}_{1}}=\left( \frac{m-em}{m+m} \right){{u}_{1}}+0 $ The velocity after collision of second sphere $ {{v}_{2}}=\left[ \frac{(1+e)m}{(m+m)} \right]{{u}_{1}}+0 $ $ \therefore $ $ \frac{{{v}_{1}}}{{{v}_{2}}}=\frac{1-e}{1+e} $