Question

The figure shows a compressed light spring and block system kept on a horizontal frictionless plane. Which of the following graph shows the correct relation between acceleration $\left(a\right)$ of block and distance $\left(x\right)$ moved by it when released till spring come to its natural state?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let $L$ be the initial compression in spring.
After travelling a distance $x$ when released, the net compression of spring will be,
$\Delta x=L-x$
Net force on block,
$F_{net}=k\Delta x$
$\Rightarrow ma=k(L-x)$
$\Rightarrow a=\frac{k}{m}(L-x)$
$\Rightarrow a=\left(\frac{-k}{m}\right)x+\frac{kL}{m}$
It is similar to the format of equation $y=mx+c$ which shows the graph of a straight line.
Here, on comparison,
Slope, $m=\frac{-k}{m}$ which is negative.
$y-$ intercept, $c=\frac{kL}{m}$ which is positive.
Hence, option $\left(c\right)$ is correct.