Question

The radiation emitted by a star $A$ is $1000$ times that of the sun. If the surface temperatures of the sun and star $A$ are $6000K$ and $2000K$, respectively, the ratio of the radii of the star $A$ and the Sun is:

• A. 300:1
• B. 600:1
• C. 900:1
• D. 1200:1

Answer 1

The correct option is C 900:1

$E\propto A{T}^4$

$\frac{E_1}{E_2}=\frac{1000}{1}=\frac{\pi {r_1}^2\times T^4}{\pi {r_2}^2\times T^4}=\frac{{r_1}^2\times T^4}{{r_2}^2\times T^4}=\frac{{r_1}^2\times {2000}^4}{{r_2}^2\times {6000}^4}=\frac{{r_1}^2}{{r_2}^2\times 81}$

$\frac{r_1}{r_2}=\sqrt{\frac{1000}{1}\times \frac{81}{1}}=284.6:1$