Question

A brick of mass $1.8$ kg is kept on a spring of spring constant $K=490N{m}^{-1}$. The spring is compressed so that after the release brick rises to $3.6$ m. Find the compression in the spring. (Take $g=10m/s^2$)

• A. 0.21 m
• B. 0.322 m
• C. 0.414 m
• D. 0.514 m

Answer 1

The correct option is D 0.514 m

As the brick raises, it gains potential energy, which is the work done by the spring on the brick.

Let the spring be compressed by $x$, then the work done is $\frac{1}{2}k{x}^2$

$\therefore \frac{1}{2}k{x}^2=mgh$

$\Rightarrow x=(\frac{2mgh}{k}{)}^{1/2}=\sqrt{\frac{2\times 1.8\times 10\times 3.6}{490}}=0.514m$

Option D.