Question

A cradle is $h$ meters above the ground at the lowest position and $H$ meters when it is at the highest point. If $v$ is the maximum speed of the swing having total mass $m$, then the relation between $h$ and $H$ is:

• A. ${mv}^2+h=H$
• B. $\frac{v^2}{2g}+h=H$
• C. $\frac{v^2}{2g}+2h=H$
• D. $\frac{v^2}{2g}+H=h$

Answer 1

The correct option is B $\frac{v^2}{2g}+h=H$

Using law of conservation of energy:
$P.E{.}_{highest}+K.E{.}_{highest}$ = $P.E{.}_{Lowest}$ + $K.E{.}_{Lowest}$
$mgH+0=mgh+\frac{1}{2}m{v}^2$
$\Rightarrow H=h+\frac{v^2}{2g}$