question_answer

Blocks \[A\] and \[B\] of mass m each are connected with spring of constant \[k\]. Both blocks lie on frictionless ground and are imparted horizontal velocity v as shown when spring is unstretched. Find the maximum stretch of spring.

A) \[v\sqrt{\frac{m}{k}}\] 

B) \[v\sqrt{\frac{m}{2k}}\]

C) \[v\sqrt{\frac{2m}{k}}\]

D) None of these

Correct Answer: A

Solution :

[a] \[\frac{1}{2}k{{x}^{2}}=2\left[ \frac{1}{2}m{{\left( \frac{v}{\sqrt{2}} \right)}^{2}} \right]\Rightarrow \frac{1}{2}k{{x}^{2}}=\frac{m{{v}^{2}}}{2}\] \[\Rightarrow x=v\sqrt{\frac{m}{k}}\][The velocities along y axis do not change]