Question

An ideal spring with spring constant k is hung from a ceiling and a block of mass M is attached to its lower end. If the mass is released with the spring initially unstretched, the maximum extension in the spring is

• A. $\frac{4Mg}{k}$
• B. $\frac{2Mg}{k}$
• C. $\frac{Mg}{k}$
• D. $\frac{Mg}{2k}$

Answer 1

The correct option is B $\frac{2Mg}{k}$

Using conservation of mechanical energy between the two position (i.e., when spring is unstretched and when elongation is maximum)

$Mgx=\frac{1}{2}k{x}^2$

(At maximum elongation velocity is 0)

$x=\frac{2Mg}{k}$