question_answer

A body of mass m is moving towards east and another body of equal mass is moving towards north. If after collision both stick together, their speed after collision would be:

A)  \[v\]                

B)  \[v/2\]

C)  \[\sqrt{2}v\]         

D)  \[v/2\sqrt{2}\]

Correct Answer: D

Solution :

 Key Idea: Momentum is conserved in inelastic collision. In inelastic collision most of the kinetic energy of the body is lost in other form (specially as heat). Thus, in inelastic collision kinetic energy is not conserved but total energy and momentum are still conserved. Hence, we have \[mv\,\hat{i}+mv\,\hat{j}=2\,mv\] \[\Rightarrow \] \[\left| 2\,mv \right|=m\,\left| v\hat{i}+v\hat{j} \right|\] \[\Rightarrow \] \[2\,mv=m\sqrt{{{v}^{2}}+{{v}^{2}}}\] \[\Rightarrow \] \[v=\frac{v\,\sqrt{2}}{2}=\frac{v}{\sqrt{2}}\].