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

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]
$\frac{\text{ Radiation cylinder }}{\text{ Radiation cube }}=\frac{2\pi r}{6a^2}=\frac{2\pi rL\cdot a}{6a^3}$
using equation (1)
We get
$\frac{R_{\text{cylinder }}}{R_{\text{cube }}}=\frac{a}{3r}$