question_answer

A sphere of mass 25 kg moving with a velocity of\[\text{4}0\text{ m}{{\text{s}}^{-\text{1}}}\]collides with another sphere of mass 15 kg which is at rest. After collision, if they move with the same velocity, find that velocity?

Answer:

\[{{m}_{1}}=25kg,\,\,{{u}_{1}}=40m/s\] \[{{m}_{2}}=15kg,\,\,{{u}_{2}}=0\] \[{{v}_{1}}={{v}_{2}}=v\] From law of conservation of momentum we know that, \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}\] \[\Rightarrow {{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}v+{{m}_{2}}v({{v}_{1}}={{v}_{2}}=v)\] \[\Rightarrow 25\times 40+15\times 0=(25+15)v\] \[\Rightarrow v=\frac{1000}{40}=25m{{s}^{-1}}\]