Q. Star $A$ has radius $r$ surface temperature $T$ while star $B$ has radius $4r$ and surface temperature $T/2$. The ratio of the power of two starts, $P_{A}:P_{B}$ is
A) 16 : 1
B) 1 : 16
C) 1 : 1
D) 1 : 4
Explanation
(c) Power $P \propto AT^{4} \propto r^{2}T^{4}$
$\Rightarrow \frac{P_{2}}{P_{1}} = \left( \frac{r_{2}}{r_{1}} \right)^{2} \times \left( \frac{T_{2}}{T_{1}} \right)^{4} = \left( \frac{4r}{r} \right)^{2} \times \left( \frac{T/2}{T} \right)^{4} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.