Question

The radiation emitted by a star $A$ is $10,000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $8000 \, K$ and $2000 \, K$ respectively. The ratio of the radii of the star $A$ and the sun is

• A. $1600:1$
• B. $1800:1$
• C. $16:1$
• D. $25:1$

Answer 1

Answer: (A)

As $E=Q=AT^{4}\Rightarrow Q=\pi r^{2}T^{4}$
$\therefore \frac{Q_{s t a r}}{Q_{s u n}}=\frac{r_{s t a r}^{2} . T_{s t a r}^{4}}{r_{s u n}^{2} . T_{s u n}^{4}}=\frac{10000}{1}$
$=\left(\frac{r_{s t a r}}{r_{s u n}}\right)^{2}\left(\frac{2000}{8000}\right)^{4}$
$10000\times 256=\left(\frac{r_{s t a r}}{r_{s u n}}\right)^{2}$
$\frac{r_{s t a r}}{r_{s u n}}=\frac{1600}{1}$