A perfectly absobing, black, solid sphere with constant density and radius R, hovers stationary above the sun. This is because the gravitational attraction of the sun is balanced by the pressure due to the sun's light. Assume the sun is far enough away that it closely approximates a point source of light. The distance from the centre of the sun at which the sphere hovers is :

Options

A. proportional to R
B. proportional to `1//R`
C. proportional to `1//R^(2)`
D. independent of R

Answer

D

Explanation

`((I)/(C))xxpiR^(2)=(GM_(s)(p(4//3)piR^(3)))/(x^(2))`
`((I)/(C))piR^(2)=GM_(s)p(4)/(3)piR^(3)`
`((E)/(t4pix^(2)))xx(1)/(C )xxpiR^(2)=(GM_(s)(p(4//3)piR^(3)))/(x^(2))`
x is independent of R