Q.
Two blocks each of mass $m$ are connected to a spring of spring constant $k.$ If both are given velocity $v$ in opposite directions, then the maximum elongation of the spring is
A) $\sqrt{\frac{mv^{2}}{k}}$
B) $\sqrt{\frac{2mv^{2}}{k}}$
C) $\sqrt{\frac{mv^{2}}{2k}}$
D) $2\sqrt{\frac{mv^{2}}{k}}$
Explanation
(b) $\frac{1}{2}mv^{2} + \frac{1}{2}mv^{2} = \frac{1}{2}kx^{2}$
$mv^{2} = \frac{1}{2}kx^{2} \Rightarrow kx^{2} = 2mv^{2} \Rightarrow x = \sqrt{\frac{2mv^{2}}{k}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.