Answer
If $r$ is smaller than $R$, then the magnitude of the force from the radiation pressure will be greater than the magnitude of the gravitational force. In this case, the particle will be blown out of the solar system.
Work Step by Step
Let $r$ be the radius of the particle.
To find the critical radius, we can equate the magnitude of the gravitational force and the force from the radiation pressure:
$\frac{G~M_s~M}{d^2} = \frac{I~A}{c}$
$\frac{G~M_s~V~\rho}{d^2} = \frac{I~\pi~r^2}{c}$
$\frac{G~M_s~\frac{4}{3}\pi~r^3~\rho}{d^2} = \frac{I~\pi~r^2}{c}$
$\frac{4~G~M_s~r~\rho}{3d^2} = \frac{I}{c}$
The critical radius $R$ is the value of $r$ which makes this equation true.
If $r$ is smaller than $R$, then the magnitude of the force from the radiation pressure will be greater than the magnitude of the gravitational force. In this case, the particle will be blown out of the solar system.
