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For two equal spheres of radius $R$, the effective radius in the Derjaguin approximation is $R_{\mathrm{eff}}=R/2$. The nonretarded attractive van der Waals potential isDifferentiating with respect to the surface gap givesThus the requested approximation gives an attraction of about $8.3$ pN. Here $h/R=2$, whereas the Derjaguin approximation requires $h\ll R$. This is the formal estimate requested by the hint, not a quantitatively reliable near-contact approximation for the printed dimensions.

A Van der Waals potential describes the separation-dependent potential energy associated with Van der Waals forces. For two neutral, nonpolar particles at separations where the nonretarded dispersion description applies, a familiar attractive contribution is $U(r)=-C_6/r^6$ with $C_6>0$. Its radial force is $-dU/dr=-6C_6/r^7$, directed toward smaller separation.

At sufficiently short separation, overlapping electronic states produce strong exchange repulsion; continuing the attractive power law to zero separation is not a physical model. A Lennard-Jones potential combines an attractive inverse-sixth-power term with a simple repulsive term to produce a finite-separation minimum. Geometry also changes the effective power law: summing pair interactions over macroscopic bodies gives different distance dependences, as in Hamaker summation. The pair potential and a measured force between extended surfaces must therefore be distinguished.