**Solution: **we know potential outside the sphere is V1 = kQ/x where x is the distance from the center x>R

and potential inside the sphere V1 = kQ/2R [3-x^{2}/R^{2}]

for center put x=0 Vo = 3kQ/2R

condition given is V1 = Vo/2

kQ/x = (3kQ/2R)/2

x=4R/3

distance from the surface is =x-R

= 4R/3 -R

=R/3