(A) : Sharper is the curvature of spot on a charged body lesser will be the surface density of charge at that point.
(R) : Electric field is zero inside a charged conductor.

$\sigma =\frac{q}{A}$

At the sharper point, the area will be lesser and the surface density is greater. Since area and surface density is inversely proportional to each other. Hence assertion is wrong

There are so many electrons within a conductor and the force of repulsion between them is also very strong. To reduce electron repulsions, electrons move to the conductor surface so the net charge inside the conductor is zero. Thus the electric field is zero inside a conductor 

The correct option is D.