According to law of gravitation
F=g*(m1*m2)/r^2
If we bring two objects close to each other say our hands then the distance will be zero and the force of attraction will become infinite because r will we zero. Therefore F will become infinite but this is not the case.
When we touch our both palms together we can easily pull then away.

Asked Ankit Sharma

Answer

When we consider the distance, it is between the center of mass of the two bodies under consideration. When we bring our hands together the distance between their CM is not zero.

Other wise, the two particles under consideration must be point masses.

Then if you consider two atoms or two nuclei, the forces that come into play will be different if we decrease the distance between two atoms or nuclei. The attraction will turn into strong repulsion when the limits are exceeded.