• # question_answer Two smooth spherical non conducting shells each of radius R having uniformly distributed charge $Q\And -\,Q$ on their surfaces are released on a smooth non-conducting surface when the distance between their centres is 5 R. The mass of A is m and that of B is 2 m. The speed of A just before A and B collide is: [Neglect gravitational interaction] $(take\,\,K=\frac{1}{4\pi {{\in }_{0}}})$ A) $\sqrt{\frac{2\,k{{Q}^{2}}}{5\,mR}}$ B) $\sqrt{\frac{4\,k{{Q}^{2}}}{5\,mR}}$ C) $\sqrt{\frac{8\,k{{Q}^{2}}}{5\,mR}}$ D) $\sqrt{\frac{16\,k{{Q}^{2}}}{5\,mR}}$

 From conservation of momentum, if speed of sphere A is v, then speed of sphere B is $\frac{v}{2}.$ From conservation of energy$\frac{1}{2}m{{v}^{2}}+\frac{1}{2}(2m)\,\,{{\left( \frac{v}{2} \right)}^{2}}=\frac{-\,k{{Q}^{2}}}{5R}+\frac{k{{Q}^{2}}}{2R}$or            $\frac{3}{4}m{{v}^{2}}=\frac{3}{10}\frac{k{{Q}^{2}}}{R}$ or         $v=\sqrt{\frac{2}{5}\frac{k{{Q}^{2}}}{mR}}$