Q. An ideal spring with spring constant $k$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is
A) $\frac{4Mg}{k}$
B) $\frac{2Mg}{k}$
C) $\frac{Mg}{k}$
D) $\frac{Mg}{2k}$
Explanation
(b) Let $x$ be the maximum extension of the spring, figure. From conservation of mechanical energy; decreases in gravitational potential energy = increase in elastic potential energy
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$Mg\ x = \frac{1}{2}k\ x^{2}$
$x = \frac{2\ Mg}{k}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.