Two spheres of the same materical have radii `1m` and `4m` and temperature `400K` and `2000K` respectively The ratio of the energy radiated per second by the first sphere to that by the second is .

Options

A. `1 :1`
B. `16:1`
C. `4:1`
D. `1:9`

Answer

A

Explanation

`(E_(1))/(E_(2))=(A_(1)T_(1)^(4))/(A_(2)T_(2)^(4))=(R_(1)^(2)T_(1)^(4))/(R_(2)^(2)T_(2)^(4))`
`=(1^(2)xx4000^(4))/(4^(2)xx2000^(4))=(16)/(16)=1`