question_answer

A body of mass \['{{m}_{1}}'\] moving with a velocity of 40 m/s hits another body of mass \[{{m}_{2}}\] which is at rest. After the impact, both the bodies move with common velocity of 30 m/s. Find the ratio of their masses.

Answer:

\[{{m}_{1}}={{m}_{1}},\,\,{{u}_{1}}=40m/s\] \[{{m}_{2}}={{m}_{2}},\,\,{{u}_{2}}=0\] \[{{v}_{1}}={{v}_{2}}=v=30m/s\] \[\Rightarrow {{m}_{1}}\times 40+{{m}_{2}}\times 0=({{m}_{1}}+{{m}_{2}})30\] \[\Rightarrow 40\,\,{{m}_{1}}=30\,\,{{m}_{1}}+30\,{{m}_{2}}\] \[\Rightarrow 40\,\,{{m}_{1}}=30\,\,{{m}_{2}}\Rightarrow \frac{{{m}_{1}}}{{{m}_{2}}}=3:1\]