Question

An explosion blows a rock into 3 pieces. Two pieces go off at right angles to each other. One of these 2 pieces of mass 1 Kg moves with 12m/s and other of mass 2 Kg moves with 8m/s. If the velocity of the 3rd piece is 40m/s, then its mass is
a) 5 Kg b)0.5 Kg c) 0.25 Kg d) 1 Kg

Answer 1

$$\begin{gathered} \mathrm{According}\mathrm{to}\mathrm{law}\mathrm{of}\mathrm{conservation}\mathrm{of}\mathrm{momentum},\mathrm{the}\mathrm{total}\mathrm{momentum}\mathrm{before} \\ \mathrm{explosion}\mathrm{is}\mathrm{equal}\mathrm{to}\mathrm{the}\mathrm{total}\mathrm{momentum}\mathrm{after}\mathrm{collision}. \\ \mathrm{Magnitude}\mathrm{of}\mathrm{momentum}\mathrm{of}\mathrm{first}\mathrm{two}\mathrm{pieces}\mathrm{which}\mathrm{are}\mathrm{going}\mathrm{perpendicular} \\ =\mathrm{Magnitude}\mathrm{of}\mathrm{momentum}\mathrm{of}\mathrm{third}\mathrm{piece} \\ \sqrt{{\left({\mathrm{m}}_1{\mathrm{v}}_1\right)}^2+{\left({\mathrm{m}}_2{\mathrm{v}}_2\right)}^2}={\mathrm{m}}_3{\mathrm{v}}_3 \\ \sqrt{{\left(1\times 12\right)}^2+{\left(2\times 8\right)}^2}={\mathrm{m}}_3\times 40 \\ {\mathrm{m}}_3=\frac{20}{40} \\ =0.5\mathrm{kg} \\ \mathbf{Ans}\mathbf{:}\mathbf{}\mathbf{Option}\mathbf{}\mathbf{-}\mathbf{}\mathbf{\left(}\mathbf{b}\mathbf{\right)} \end{gathered}$$