KVPY SX SB Exam 19-Nov-2017 Question Paper

The planet should be in Thermal equilibrium with star.
Amount of heat energy emitted by start per second E1=(σT*4)(4πR*2)
∵ d = distance between star and planet
Hence, amount of energy reaching planet per unit area per second =

E1

4πd2

=

(σT*4)(4πR*2)

4πd2

=

σT*2R*2

d2

Henceenergy received by planet per second
E2=(

σT*4R*2

d2

)πRP2
T = Temperature of planet then amount of
energy emitted by planet per second
E3=(σT4)(4πRP2)
For thermal equilibrium E3=E2
⇒ (σT4)(4πRP2)=

(σT*4R*2)

d2

(πRP2)
⇒ T4=

T*4R*2

4d2

⇒ T=T*√

R*

2d

=fT*
⇒ f∝√

R*

d

Hence correct answer is (A)