question_answer

A body of mass (4w) is lying in \[xy\]-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass (m) move perpendicular to each other with equal speeds\[(\upsilon )\]. The total kinetic energy generated due to explosion is  [AIPMT 2014]

A)  \[m{{v}^{2}}\]            

B)  \[\frac{3}{2}m{{v}^{2}}\]

C)  \[2m{{v}^{2}}\]           

D)  \[4m{{v}^{2}}\]

Correct Answer: D

Solution :

According to question, the third part of mass 2m will move as shown in the figure, because the total momentum of the system after explosion must remain zero. Let the velocity of third part is v'. From the conservation of momentum \[\sqrt{2}(mv)=(2m)\times v'\Rightarrow v'=\frac{v}{\sqrt{2}}\] \[\Rightarrow \] So total kinetic energy generated by the explosion \[=\frac{1}{2}m{{v}^{2}}+\frac{1}{2}m{{v}^{2}}+\frac{1}{2}(2m)v{{'}^{2}}\] \[=m{{v}^{2}}+m\times {{\left( \frac{v}{\sqrt{2}} \right)}^{2}}\] \[=m{{v}^{2}}+\frac{m{{v}^{2}}}{2}=\frac{3}{2}m{{v}^{2}}\]