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:

Use the principle of conservation of mechanical energy. Let the maximum extension be $x$.Loss in gravitational potential energy of the block = $Mgx$.Gain in elastic potential energy of the spring = $\frac{1}{2}k{x}^2$.At maximum extension, the block momentarily comes to rest, so the change in kinetic energy is zero.
$$Mgx=\frac{1}{2}k{x}^2$$
Assuming $x\ne 0$:
$$Mg=\frac{1}{2}kx$$
$$x=\frac{2Mg}{k}$$