This question has been asked several times on this site. However, most of the answers were qualitative in nature.

Suppose a body is placed at a point on earth's surface at latitude $\theta$ from the axis. The body will experience a centripetal force, when observed from an inertial frame. The question is to find the normal force that will be exerted by the ground, i.e the apparent weight of the body.

My questions are $-$

$1:$ I believe the normal force and true gravitational force will not be collinear unless at the equator or at poles. If this is correct, what will the angle between them be?

$2:$ Will the direction of perceived gravity be same as that of the normal force?

$3.$ What will the magnitude of normal force be?

I can analyse the situation from a rotating frame, by adding a centrifugal force, but cannot reach to the same result from a inertial frame.

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Excuse the poor diagram.