question_answer

A body of mass 2 kg moving with uniform velocity of 40 m/s collides with another body at rest. If the two bodies move together with a velocity of 25 m/s. Find the mass of the other body.

Answer:

\[{{m}_{1}}=2\,\,kg,\,\,{{u}_{1}}=40m/s\] \[{{m}_{2}}=?\] \[{{u}_{2}}=0\] \[{{v}_{1}}={{v}_{2}}=v=25m/s\] \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}\] \[\Rightarrow {{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}=v({{m}_{1}}+{{m}_{2}})\] \[\Rightarrow 2\times 40+{{m}_{2}}\times 0=25(2+{{m}_{2}})\] \[\Rightarrow 80=50+25{{m}_{2}}\Rightarrow 25{{m}_{2}}=80-50\] \[\Rightarrow {{m}_{2}}=1.2kg\]