Two spheres of the same material having radii `r` and `4r` and temperature `2T_(0)` and `T_(0)` respectively. The ratio of rate of radiation of energy by the sphere is

Options

A. `1:1`
B. `1:2`
C. `2:1`
D. `3:1`

Explanation

(a) Energy radiated per second `P=esigmaAT^(4)`
`:.(P_(1))/(P_(2))=(A_(1)T_(1)^(4))/(A_(2)T_(2)^(4))=((4pir^(2))/(4pi(4r)^(2)))(16T_(0)^(4))/(T_(0)^(4))=(r^(2))/(16r^(2))xx(16T_(0)^(4))/(T_(0)^(4))=1:1`