Question

A compressed spring of spring constant $k$ releases a ball of mass $m$. If the height of spring from the ground is $h$ and the spring is compressed through a distance $x$, then the horizontal distance covered by ball to reach the ground is

• A. $\sqrt{\frac{kh}{mg}}$
• B. $\frac{xkh}{mg}$
• C. $x\sqrt{\frac{2kh}{mg}}$
• D. $\frac{mg}{x\sqrt{kh}}$

Answer 1

Answer: (C)

$x\sqrt{\frac{2kh}{mg}}$

Spring energy $=$ kinetic energy
i.e. $\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2$ or $v=x\sqrt{\frac{k}{m}}$
Time taken by ball to reach ground, t
$=\sqrt{\frac{2h}{g}}$ (from $S=ut+\frac{1}{2}a{t}^2$)
$\therefore$ Horizontal distance covered $=vt$
$=x\sqrt{\frac{k}{m}}\sqrt{\frac{2h}{g}}=x\sqrt{\frac{2kh}{mg}}$