Question

57. A space craft of mass M and moving with the velocity v suddenly breaks into two pieces of same mass m. After the explosion one of the mass m becomes stationary . What is the velocity of other part of craft
1.Mv/M-m
2.v
3.Mv/m
4.(M-m )v/m
​both options 1. and 3. should be correct because of equal masses.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{mass}\mathrm{of}\mathrm{space}\mathrm{craft}=\mathrm{M} \\ \mathrm{velocity}\mathrm{of}\mathrm{space}\mathrm{craft}=\mathrm{v} \\ \mathrm{Initial}\mathrm{momentum},{\mathrm{P}}_{\mathrm{i}}=\mathrm{Mv} \\ \mathrm{After}\mathrm{explosion},\mathrm{the}\mathrm{masses}\mathrm{of}\mathrm{the}\mathrm{parts}\mathrm{are}\mathrm{m}\mathrm{and}\mathrm{M}-\mathrm{m}. \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question},\mathrm{m}\mathrm{becomes}\mathrm{stationary}. \\ \mathrm{Let}\mathrm{the}\mathrm{velocity}\mathrm{of}\mathrm{other}\mathrm{part}\mathrm{is}\mathrm{v}\text{'}. \\ \mathrm{Total}\mathrm{momentum}\mathrm{after}\mathrm{explosion},{\mathrm{P}}_{\mathrm{f}}=\mathrm{m}\times 0+\left(\mathrm{M}-\mathrm{m}\right)\mathrm{v}\text{'} \\ {\mathrm{P}}_{\mathrm{f}}=\left(\mathrm{M}-\mathrm{m}\right)\mathrm{v}\text{'} \\ \mathrm{By}\mathrm{law}\mathrm{of}\mathrm{conservation}\mathrm{of}\mathrm{momentum}, \\ {\mathrm{P}}_{\mathrm{f}}={\mathrm{P}}_{\mathrm{i}} \\ \left(\mathrm{M}-\mathrm{m}\right)\mathrm{v}\text{'}=\mathrm{Mv} \\ \mathrm{v}\text{'}=\frac{\mathrm{Mv}}{\left(\mathrm{M}-\mathrm{m}\right)} \end{gathered}$$