Question

An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released suddenly with the spring initially unstretched. Then 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

$\frac{2Mg}{k}$

The decrease in potential energy of the block = increase in elastic potential energy of the spring

$\therefore Mg{x}_{max}=\frac{1}{2}k{x}^{2}max$

$\Rightarrow x_{max}=\frac{2Mg}{k}$