A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and…
A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value $k$. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be
$M g / k$
$2 \mathrm{Mg} / \mathrm{k}$
$4 \mathrm{Mg} / \mathrm{k}$
$M g / 2 k$
Solution
Key Idea Use the law of conservation of energy. Let $x$ be the extension in the spring.
Applying conservation of energy
$\begin{array}{ll}
& \mathrm{mgx}-\frac{1}{2} \mathrm{kx}^2=0-0 \\
\Rightarrow \quad & \mathrm{x}=\frac{2 \mathrm{mg}}{\mathrm{k}}
\end{array}$