The radiation emitted by a star A is 10000 times that of the sun. If the surface temperatures of the sun and star A are 6000 K and 2000 K respectively, the ratio of the radii of the star A and the sun is

Question

The radiation emitted by a star A is 10000 times that of the sun. If the surface temperatures of the sun and star A are 6000 K and 2000 K 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

Tardigrade Admin · Accepted Answer

ϵ propto AT4 ; ϵ propto R2T4 Or R propto √(ϵ /T4) (R2/R1)=√(ε2/ε1) ⋅ (T14/T24)=√(10000/1) ×((6000/2000))4 =(10)2× ((3/1))2=900:1

Q. The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and star $A$ are $6000 K$ and $2000 K$ respectively, the ratio of the radii of the star $A$ and the sun is

$300 : 1$

$600 : 1$

$900 : 1$

$1200 : 1$

$ϵ \propto A T^{4}; ϵ \propto R^{2} T^{4}$ Or $R \propto \frac{ϵ}{T ^{4}}$
$\frac{R _{2}}{R _{1}} = \frac{ε _{2}}{ε _{1}} \cdot \frac{T _{1}^{4}}{T _{2}^{4}} = \frac{10000}{1} \times (\frac{6000}{2000})^{4}$
$= (10)^{2} \times (\frac{3}{1})^{2} = 900 : 1$

Q. The radiation emitted by a star A is 10000 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

300:1

600:1

900:1

1200:1