Question

A wax candle floats vertically in a liquid of density twice that of wax. The candle burns at the rate of $4\, cm / h$. Then with respect to the surface of the liquid, the upper end of the candle will fall at the rate of $k\, cm / h$. Find $k$.

Answer 1

$V_{\text {in }} \rho_{\text {water }} g=V_{\text {out }} \rho_{\text {wax }} g, V_{\text {out }}=\frac{V}{2}$
$A h=\frac{A L}{2}, \frac{d h}{d t}=\frac{1}{2} \frac{d L}{d t}=2 \,cm / h$