Question

A smooth block of mass $10\text{kg}$ is released from rest from a height $5\text{m}$. It slides and compresses the spring of stiffness as shown in figure $200\frac{\text{N}}{\text{m}}.$ The maximum compression of the spring is

• A. $2\sqrt{5}\text{m}$
• B. $\sqrt{5}\text{m}$
• C. $\sqrt{2.5}\text{m}$
• D. $0$

Answer 1

The correct option is B $\sqrt{5}\text{m}$

Using law of conservation of energy.
$\Delta K=-\Delta U$
Since, block starts from rest and the block will come to rest at the time of maximum Compression $\Delta K=0.$
$\Rightarrow \Delta U=0$
Taking spring and block as one system
$\Delta U=(\Delta U{)}_{\text{s}pring}+(\Delta U{)}_{\text{g}ravity}=0.$
$(\Delta U{)}_{\text{s}pring}=-(\Delta U{)}_{\text{g}ravity}$
$\frac{1}{2}k{x}^2-0=-(0-mgh)\Rightarrow \frac{1}{2}k{x}^2=mgh$
Then $x=\sqrt{\frac{2mgh}{k}}=\sqrt{\frac{2\times 10\times 10\times 5}{200}}=\sqrt{5}\text{m}$