A charge is kept close to a metal sphere of radius R.What is the potential at point P at a distance R/2 above the centre due to charges induced on the sphere?

anything multiplied by zero will give always a zero result....

potential remains same inside a conducting sphere...

TOTAL V at centre =kq/x+kQ/R-kQ/R=kq/x

Q=CHARGE INDUCED..

now V at centre=V at point P

V at P=kq/(R/2^2+x^2)^1/2 +V'

V'=V by induced charges at P

so    kq/x=V'+ kq/(R/2^2+x^2)^1/2

we get  V'