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

Correct Answer: D

Solution :

[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        \[{{F}_{\max }}\propto \sqrt{k}\propto \sqrt{m}\propto {{v}_{0}}\]