• # question_answer A block of mass m moving with a velocity ${{v}_{0}}$on a smooth horizontal floor collides with a light spring of stiffhess k that is rigidly fixed horizontally with a vertical wall. If the maximum force imparted by the spring on the block is F, then A) $F\propto \sqrt{m}$ B) $F\propto \sqrt{k}$ C) $F\propto {{v}_{0}}$ D) None of these

 [d] Energy conservation between the positions A and B requires that $\Lambda PE+KE=0$ or         $\frac{1}{2}k{{x}^{2}}-\frac{1}{2}mv_{0}^{2}=0$ $\therefore$ $x=\sqrt{\frac{m}{k}}{{v}_{0}}$ $\therefore \,\,\,\,\,\,{{F}_{\max }}=kx=\sqrt{mk}{{v}_{0}}$ or        ${{F}_{\max }}\propto \sqrt{k}\propto \sqrt{m}\propto {{v}_{0}}$