Physics - Center of Mass Question with Solution | TestHub

Along the line of impact 2 kg sphere is having velocity $2\sqrt{3}\mathrm{m}/\mathrm{s}$ and 4 kg sphere is having velocity $-\sqrt{3}m/s$. VCM along the line impact is zero $2\times 2\sqrt{3}-4\sqrt{3}=2V_1+4V_2$ (along line of impact) $\therefore V_1+2V_2=0$ $e=\frac{V_2-V_1}{V_1-V_2}=\frac{V_2-V_1}{2\sqrt{3}+\sqrt{3}}\Rightarrow V_2-V_1=\sqrt{3}$ From (1) and (2) $V_2=\frac{1}{\sqrt{3}}\mathrm{m}/s;V_1=-\frac{2}{\sqrt{3}}\mathrm{m}/\mathrm{s}$ Impulse of reformation of 2 kg is $J_R=2\left(V_1-0\right)=-\frac{4}{\sqrt{3}}N-s$ Maximum potential energy of deformation is loss in kinetic energy during deformation along the line of impact $U=\frac{1}{2}(2)(2\sqrt{3}{)}^2+\frac{1}{2}(4)(\sqrt{3}{)}^2-\frac{1}{2}(6{)}^2{}_{VCM}=12+6=18J$.