Question

if potential at the surface of earth is assigned zero value,then potential at centre of earth

Answer 1

What ever will be the potential at the surface of the earth, the same potential will be found at the center of the earth. As the amount of work which will be performed in bringing the unit positive charge to the center of the earth will be zero. 
So this is the reason, the potential at the center will also be zero. 

Answer 2

Explanation:

refer to the attachment above