Question

A block of mass $m$ is suddenly released from the top of a spring of stiffness constant $k$. Given acceleration due to gravity is $=g$, then
(i) the maximum compression in the spring and
(ii) the compression in the spring at equilibrium respectively are

• A. $\frac{2mg}{k},\frac{mg}{k}$
• B. $\frac{mg}{k},\frac{mg}{k}$
• C. $\frac{mg}{k},\frac{2mg}{k}$
• D. $\frac{2mg}{k},\frac{2mg}{k}$

Answer 1

The correct option is A $\frac{2mg}{k},\frac{mg}{k}$

Max. compression $mgx=\frac{1}{2}k{x}^2$
$x=\frac{2mg}{k}$
At equilibrium $mg=kx$
$x=\frac{mg}{k}$