Question

A body of mass 4m lying in xy plane at rest. It suddenly explodes into 3 pieces each of mass m move perpendicular to each other with equal speeds v . The total K.E. generated due to explosion is
a) mv²
b)3/2 mv²
c)2mv²
d)4mv²

Answer 1

$$\begin{gathered} \mathrm{From}\mathrm{the}\mathrm{law}\mathrm{of}\mathrm{conservation}\mathrm{of}\mathrm{momentum}, \\ \mathrm{Magnitude}\mathrm{of}\mathrm{the}\mathrm{momentum}\mathrm{of}\mathrm{heavier}\mathrm{piece}\mathrm{of}\mathrm{mass}2\mathrm{m}= \\ \mathrm{Magnitude}\mathrm{of}\mathrm{the}\mathrm{vector}\mathrm{sum}\mathrm{of}\mathrm{moemntum}\mathrm{of}\mathrm{each}\mathrm{peice}\mathrm{of}\mathrm{mass}\mathrm{m} \\ \left(2\mathrm{m}\right)\mathrm{v}\text{'}=\sqrt{{\left(\mathrm{mv}\right)}^2+{\left(\mathrm{mv}\right)}^2} \\ \left(2\mathrm{m}\right)\mathrm{v}\text{'}=\sqrt{2}\mathrm{mv} \\ \left(2\right)\mathrm{v}\text{'}=\sqrt{2}\mathrm{v} \\ \mathrm{v}\text{'}=\frac{\mathrm{v}}{\sqrt{2}} \\ \mathrm{KE}\mathrm{generated}: \\ \mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^2+\frac{1}{2}{\mathrm{mv}}^2+\frac{1}{2}\left(2\mathrm{m}\right){\left(\mathrm{v}\text{'}\right)}^2 \\ =\frac{1}{2}\left({\mathrm{mv}}^2+{\mathrm{mv}}^2+\left(2\mathrm{m}\right)\left(\frac{{\mathrm{v}}^2}{2}\right)\right) \\ =\frac{1}{2}\left(3{\mathrm{mv}}^2\right) \\ \mathbf{Ans}\mathbf{:}\mathbf{}\mathbf{Option}\mathbf{}\mathbf{-}\mathbf{}\mathbf{\left(}\mathbf{b}\mathbf{\right)} \end{gathered}$$