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

Answer: (B)

$\frac{1-e}{1+e}$

Answer 2

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 ${{v}_{2}}=\left[ \frac{(1+e)m}{(m+m)} \right]{{u}_{1}}+0$ $\therefore$ $\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{1-e}{1+e}$