Answer to Question #9984 in Mechanics | Relativity for leon

Question

if radius of the earth (assuming perfect sphere)is decreased keeping its mass constant ,effective value of g will increase at poles while may increase or decrease at equator.WHY??

Answer 1

g = G*M / R^2
The value of g changes from place to place due to the
elliptical shape
of the Earth and the rotation of the Earth. Due to the shape
of the
Earth, g is inversely proportional to the square of the radius.
It
is least at the equator and maximum at the poles, since the
equatorial radius
(6378.2 km) is more than the polar radius (6356.8
km)