Answer
$a = 1.5\times 10^{-9}~m/s^2$
Work Step by Step
We can find the force to due radiation pressure:
$F = \frac{I~A}{c}$
$F = \frac{I~\pi~r^2}{c}$
$F = \frac{(6.0\times 10^{-3}~W/m^2)~(\pi)~(2.0\times 10^{-6}~m)^2}{3.0\times 10^8~m/s}$
$F = 2.513\times 10^{-22}~N$
We can find the mass of the sphere:
$M = V~\rho$
$M = \frac{4}{3}\pi~r^3~\rho$
$M = (\frac{4}{3}\pi)~(2.0\times 10^{-6}~m)^3~(5.0\times 10^3~kg/m^3)$
$M = 1.68\times 10^{-13}~kg$
We can find the acceleration:
$F = Ma$
$a = \frac{F}{M}$
$a = \frac{2.513\times 10^{-22}~N}{1.68\times 10^{-13}~kg}$
$a = 1.5\times 10^{-9}~m/s^2$
