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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
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Verified Answer
The correct answer is:
$2 \mathrm{Mg} / \mathrm{k}$
Key Idea Use the law of conservation of energy. Let $x$ be the extension in the spring.
Applying conservation of energy
$$
\begin{array}{ll}
& \mathrm{mgx}-\frac{1}{2} \mathrm{kx}^2=0-0 \\
\Rightarrow \quad & \mathrm{x}=\frac{2 \mathrm{mg}}{\mathrm{k}}
\end{array}
$$
Applying conservation of energy
$$
\begin{array}{ll}
& \mathrm{mgx}-\frac{1}{2} \mathrm{kx}^2=0-0 \\
\Rightarrow \quad & \mathrm{x}=\frac{2 \mathrm{mg}}{\mathrm{k}}
\end{array}
$$
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