Question

Two black spheres 'P' and 'Q' have radii in the ratio 3 : 2. The wavelengths of maximum intensity radiation are in the ratio 3 : 4 respectively. The ratio of radiated power by 'P' to 'Q' is ______.

Options

• `25/9`

• `74/9`

• `16/9`

• `64/9`

Answer 1

Two black spheres 'P' and 'Q' have radii in the ratio 3 : 2. The wavelengths of maximum intensity radiation are in the ratio 3 : 4 respectively. The ratio of radiated power by 'P' to 'Q' is `underline(64/9)`.

Explanation:

Power P = σAT⁴

= σ × 4πR² × T⁴

`thereforeP_1/P_2=R_1^2/R_2^2 T_1^4/T_2^4=R_1^2/R_2^2(lambda_2/lambda_1)^4`           `[becauselambda prop1/T]`

`=(3/2)^2*(4/3)^4=9/4xx(4xx64)/(9xx9)=64/9`