Question

A solid cylinder of length $L$ and radius $r$ is heat upto same temperature as that of a cube of edge length $a$. If both have same material, volume and allowed to cool under similar conditions, then ratio of amount of radiations radiated will be (Neglect radiation emitted from flat surfaces of the cylinder)

• A. $\frac{a}{3 r}$
• B. $\frac{2 a}{r L}$
• C. $\frac{a^{2}}{r L}$
• D. $\frac{\pi a^{2}}{2 r L}$

Answer 1

Answer: (A)

$\because$ Both have same volume
$\therefore a^{3}=\pi r^{2} L\,\,\,...(1)$
Amount of radiation $\propto$ Surface area
[ $\because$ Temperature, material are same for both]
$\frac{\text { Radiation cylinder }}{\text { Radiation cube }}=\frac{2 \pi r}{6 a^{2}}=\frac{2 \pi r L \cdot a}{6 a^{3}}$
using equation (1)
We get
$\frac{R_{\text {cylinder }}}{R_{\text {cube }}}=\frac{a}{3 r}$