Two stars A and B at equal surface temperature. Star A has surface area four times that of B. The ratio in the luminosities of A and B will be

Question

Two stars A and B at equal surface temperature. Star A has surface area four times that of B. The ratio in the luminosities of A and B will be (A)  beginmatrix 1 16 endmatrix  (B)  beginmatrix 1 4 endmatrix  (C)  beginmatrix 16 1 endmatrix  (D)  beginmatrix 4 1 endmatrix

Tardigrade Admin · Accepted Answer

: Luminosity of a star L=σ 4π R2T4 ∴ (LA/LB)=(Surface text area text of text star text A/Surface text area text of text star text B) ∴ (LA/LB)=(4/1)

Q. Two stars A and B at equal surface temperature. Star A has surface area four times that of B. The ratio in the luminosities of A and B will be

$116$

$14$

$161$

$41$

: Luminosity of a star $L = σ 4 π R^{2} T^{4}$ $∴$ $\frac{L _{A}}{L _{B}} = \frac{S u r f a ce a re a o f s t a r A}{S u r f a ce a re a o f s t a r B}$ $∴$ $\frac{L _{A}}{L _{B}} = \frac{4}{1}$

Q. Two stars A and B at equal surface temperature. Star A has surface area four times that of B. The ratio in the luminosities of A and B will be

1​16​

1​4​

16​1​

4​1​

: Luminosity of a star L=σ4πR2T4 ∴ LB​LA​​=SurfaceareaofstarBSurfaceareaofstarA​ ∴ LB​LA​​=14​

$116$

$14$

$161$

$41$

: Luminosity of a star $L = σ 4 π R^{2} T^{4}$ $∴$ $\frac{L _{A}}{L _{B}} = \frac{S u r f a ce a re a o f s t a r A}{S u r f a ce a re a o f s t a r B}$ $∴$ $\frac{L _{A}}{L _{B}} = \frac{4}{1}$