KVPY 2019 SB SX Exam Previous Papers

Question : 28 of 120

Marks: +1, -0

A certain stellar body has radius 50 Rs and temperature 2T

_s

and is at a distance of 2 × 10

^{10}

A. U. from the earth. Here A.U. refers to the earth sun distance and R

_s

and T

_s

refer to the sun's radius and temperature respectively. Take both star and sun to be ideal black bodies. The ratio of the power received on earth from the stellar body as compared to that received from the sun is close to

4 × 10 $^{–20 }$
2 × 10 $^{–6}$
10 $^{–8}$
10 $^{–16}$

Validate

Solution:

P_\body =σ(4π(50R_s)^2)(2T_s)^4

⇒

P_\body=P_\sun × (50)^2 × (2)^4

Intensity at earth due to body =

{P_\body}/{{4πR^2}_\body}={ (50)^2 × (2)^4×P_\sun }/{4×10^20×(4πAU)^2}

⇒

I_\body = 10^{–16} × I_\sun

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