The answer depends on the size and mass of the ball. It also depends on its ability to reflect light (albedo $A$), but let's forget that for a moment.
Pressure vs. gravity
Solar pressure decreases with $R^2$ (the inverse square law). At Earth, which is located at a distance of $1,mathrm{AU}$ from the Sun, we receive an irradiance $S_0 = 1361,mathrm{W},mathrm{m}^{-2}$. Since the momentum of a photon of energy $E$ is $p = E/c$, the pressure at a distance $R$ from the Sun is
$$
P = frac{S_0}{c(R/mathrm{AU})^2}.
$$
If the ball's radius is $r$, this pressure will exert a force
$$
F_gamma = pi r^2 P = frac{pi r^2 S_0}{c (R/mathrm{AU})^2}qquad(mathrm{away,from,the,Sun}).
$$
Meanwhile, if the ball's mass is $m$, the gravitational force exerted by the Sun on the ball is
$$
F_g = frac{G M_odot m}{R^2},qquad(mathrm{toward,the,Sun})
$$
where $G$ is the gravitational constant and $M_odot$ is the mass of the Sun.
Threshold for falling
The threshold for the ball falling into the Sun is found by equating the two oppositely directed forces:
$$
frac{pi r^2 S_0}{c (R/mathrm{AU})^2} = frac{G M_odot m}{R^2}.
$$
The first thing to notice is that $R$ cancels out; the reason being that flux density and gravity both follow the inverse square law. Second, re-arranging terms we see that the ball will fall if its mass per area is greater than this threshold (if I have calculated correctly):
$$
frac{m}{r^2} gtrsim frac{pi S_0}{c G M_odot } mathrm{AU}^2 simeq 2.4times10^{-4},mathrm{g},mathrm{cm}^{-2}.
$$
Now you can plug in your favorite numbers. You will find that for most macroscopic objects, such as a football, a rock, and even a sand grain, it will fall. On the other hand, small "balls" such as dust grains and atoms, will tend to be pushed away from the Sun. An example of a macroscopic object that won't fall is a solar sail which seeks to maximize area per mass.
For a given density, say $rho = 2.5,mathrm{g},mathrm{cm}^{-3}$ which is characteristic of rocky materials, you can also calculate the maximum size before it falls toward the Sun:
$$
r_mathrm{max} = frac{3}{4pirho} ,(2.4times10^{-4},mathrm{g},mathrm{cm}^{-2}) sim 0.1mathrm{-}1,mumathrm{m}.
$$
Albedo
The above calculations hold of all the radiation is absorbed by the object. If a fraction of it is reflected, the radiation will transfer more momentum to the object, and for a prefectly reflecting object, the radiation force will be roughly twice the amount above (the exact factor depends on the geometry of the object).
Extinction curves
It should be noted, though, that treating small particles as rigid spheres with a geometric cross section becomes imprecise when their size is comparable to wavelength of the light; rather, their absorption/scattering cross section should be treated quantum mechanically. In practice, extinction curves — i.e. the cross section as a function of the wavelength of the light for a given dust particle size distribution — are measured observationally by comparing the light from unobscured star with similar stars behind dust clouds, and subsequently fitted with various functional forms.