How to find the centripetal acceleration of an object that is at a latitude of 52 degree to the equator given the radius of earth=6400km and angular vel of Earth about its axis=7.3 x 10^-5 rad/s ?

Answer 1

find the radius of motion at latitude 52deg. At zero latitude, rad=re, at latitude theta, rad=re*cosineTheta.

So you know ang velocity, radius

Centripetal acceleration=w^2*r

remember the radius of motion is the distance from the Point on the surface to the AXIS of rotaion, not the distance to the center of the Earth.