MCQ
Star $A$ has radius $r$ surface temperature $T$ while star $B$ has radius $4 r$ and surface temperature $7 / 2$. The ratio of the power of two starts, $P$. $: P$ is
- A$16: 1$
- B$1: 16$
- ✓$1: 1$
- D$1: 4$
✓
Answer
Correct option: C.
$1: 1$
Power $P \propto A T^4 \propto r^2 T^4$
$\Rightarrow \frac{P_2}{P_1}=\left(\frac{r_2}{r_1}\right)^2\times\left(\frac{T_2}{T_1}\right)^4=\left(\frac{4r}{r}\right)^2\times\left(\frac{T / 2}{T}\right)^4=\mathrm{l} .$
$\Rightarrow \frac{P_2}{P_1}=\left(\frac{r_2}{r_1}\right)^2\times\left(\frac{T_2}{T_1}\right)^4=\left(\frac{4r}{r}\right)^2\times\left(\frac{T / 2}{T}\right)^4=\mathrm{l} .$
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