Question

An ideal spring of spring-constant $k$, is suspended from the ceiling of a room and a block of mass $M$ is fastened to its lower end. If the block is released when the spring is unstretched then the maximum extension in the spring is

• A. $4Mg/k$
• B. $2Mg/k$
• C. $Mg/k$
• D. $Mg/2k$

Answer 1

The correct option is B $2Mg/k$

Maximum extension be $x$

Conservation of energy gives,

decrease in potential energy of mass= increase of potential spring

$\Rightarrow mgx=\frac{1}{2}k{x}^2$

$\Rightarrow x=\frac{2mg}{k}$