g= acceleration due to gravity.
R= radius of earth
d= depth a below earth surface at which the acceleration due to gravity is same at the equator and the poles.
geff due to rotation =geff due to depth
g−ω2R=g(1−dR)
g−Rω2=g−gdR
−Rω2=−gdR
d=ω2R2g
The correct option is A.