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  4. 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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Q. 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

AIPMTAIPMT 2009Work, Energy and Power

Solution:

When the mass attached to a spring fixed at the other end is allowed to fall suddenly, it extends the spring by $x$. Potential energy lost by the mass is gained by the spring.
$M g x=\frac{1}{2} k x^{2}$
$ \Rightarrow x=\frac{2 M g}{k} .$