Question

Two spheres of the same material have radii 1m and 4m and temperature 4000 K and 2000 K respectively. Ratio of the energy radiated per second by the first sphere to that by the second is ........... . (A) 1 : 1 (B) 16 : 1 (C) 4 : 1 (D) 1 : 9

Answer 1

Answer:

option A is correct

Explanation:

pls refer attachment

Answer 2

Answer:

Option (A) is correct.

Explanation:

Since we know that the energy radiated by the body is proportional to the temperature to the power four and square of the radius of the sphere.

$E\alpha r^{2} T^{4}$

So, ratio of the energy radiated per second by the first sphere to second sphere is

$\dfrac{E_{1} }{E_{2} } = \dfrac{r_{1} ^{2}T_{1}^{4} }{r_{2} ^{2}T_{2}^{4}}$

So,

$\dfrac{E_{1} }{E_{2} } = \dfrac{1^{2}4000^{4}}{4^{2} 2000^{4} } =\dfrac{1}{1}$

So, option (A) is correct.