Question
A ball of mass $$m$$ moving with a constant velocity strikes against a ball of same mass at rest. If $$e = $$ coefficient of restitution, then what will be the ratio of velocity of two balls after collision?
A.
$$\frac{{1 - e}}{{1 + e}}$$
B.
$$\frac{{e - 1}}{{e + 1}}$$
C.
$$\frac{{1 + e}}{{1 - e}}$$
D.
$$\frac{{2 + e}}{{e - 1}}$$
Answer :
$$\frac{{1 - e}}{{1 + e}}$$
Solution :
$$\eqalign{
& {\text{As}}\,{u_2} = 0\,{\text{and}}\,{m_1} = {m_2},{\text{therefore}}\,{\text{from}} \cr
& {m_1}{u_1} + {m_2}{u_2} = {m_1}{v_1} + {m_2}{v_2} \cr
& {\text{we}}\,{\text{get}}\,{u_1} = {v_1} + {v_2} \cr
& {\text{Also,}}\,e = \frac{{{v_2} - {v_1}}}{{{u_1}}} = \frac{{{v_2} - {v_1}}}{{{v_2} + {v_1}}} = \frac{{\frac{{1 - {v_1}}}{{{v_2}}}}}{{\frac{{1 + {v_1}}}{{{v_2}}}}}, \cr
& {\text{which}}\,{\text{gives}}\,\frac{{{v_1}}}{{{v_2}}} = \frac{{1 - e}}{{1 + e}} \cr} $$