A hot black body emits the energy at the rate of `16 J m^(-2) s^(-1)` and its most intense radiation corresponds to suspension is vertically above the centre of the sphere. A torque of 0.10 N-m is required to rotate the sphere through an angle of `1.0` rad and then maintain the orientation. If the sphere is then released, its time period of the oscillation will be :

Options

A. 4
B. 1
C. 64
D. 256

Answer

D

Explanation

Wein's displacement law is :
`lambda_(m) . T = b` i.e. `T prop (1)/(lambda_(m))`
Here `lambda_(m)` becomes half
`:.` Temperature doubles.
Also `e = sigma T^(4)`
`rArr (e_(1))/(e_(2)) = (T_(1))/(T_(2))^(4) rArr e_(2) = (T_(1))/(T_(2))^(4) e`,
`= (2)^(4) 16 = 16.16 = 256J m^(-2) s^(-1)`