A toy gun consists of a spring and a  rubber dart of mass 16g. When compressed by 4cm and released, it projects the dart to a height of 2m. If compressed by 6cm, the height achieved is

 If k is the spring factor, then P.E of the spring compressed by distance $x\left(=\frac{1}{2}k{x}^2\right)$  will equal to gain in P.E. of the dart $\left(=mgh\right)$  i.e. $\frac{1}{2}k{x}^2=mgh$ 

$\therefore \frac{1}{2}k{\left(4\right)}^2=16\times g\times \mathrm{200...................}\left(i\right)$

And $\frac{1}{2}k{\left(6\right)}^2=16\times g\times h\mathrm{...................}\left(ii\right)$

On solving , (i) and (ii), we get h = 450cm = 4.5m.

$\left(h+x\right)\alpha x^2$   $\because mg\left(h+x\right)=\frac{k x^2}{2}$