question_answer

A body of mass \[{{m}_{1}}\] moving with a velocity 3 ms?1 collides with another body at rest of mass \[{{m}_{2}}.\]After collision the velocities of the two bodies are 2 ms?1 and 5ms?1 respectively along the direction of motion of \[{{m}_{1}}\] The ratio \[{{m}_{1}}/{{m}_{2}}\] is             [EAMCET (Engg.) 2000]

A)          \[\frac{5}{12}\]            

B)          \[5\]

C)          \[\frac{1}{5}\]              

D)          \[\frac{12}{5}\]

Correct Answer: B

Solution :

If target is at rest then final velocity of bodies are \[{{v}_{1}}=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)\ {{u}_{1}}\] ?(i) and \[{{v}_{2}}=\frac{2{{m}_{1}}{{u}_{1}}}{{{m}_{1}}+{{m}_{2}}}\]           ?(ii) From (i) and (ii) \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{m}_{1}}-{{m}_{2}}}{2{{m}_{1}}}=\frac{2}{5}\]Þ\[\frac{{{m}_{1}}}{{{m}_{2}}}=5\]