Question

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 in an unstretched condition. Then, the maximum extension in the block from its mean position will be,

• A. $4\frac{M g}{K}$
• B. $2\frac{M g}{K}$
• C. $\frac{M g}{K}$
• D. $\frac{M g}{2 K}$

Answer 1

Answer: (B)

Let $x$ be the maximum extension of the spring.
From energy conservation,
loss in gravitational potential energy $=$ gain in potential energy of spring.
$Mgx=\frac{1}{2}Kx^{2}$
$\Rightarrow $ $x=\frac{2 M g}{K}$ .