Q. A body of mass (4m) is lying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is :
A) $mv^2$
B) $\frac{3}{2}mv^2$
C) $2mv^2$
D) $4mv^2$
Explanation
[Solution] The third piece (2m) carries momentum $\sqrt{2}mv$, so its speed is $\frac{v}{\sqrt{2}}$. KE = $\frac{1}{2}mv^2 \times 2 + \frac{1}{2}(2m)\frac{v^2}{2} = \frac{3}{2}mv^2$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.