Question

The apparent value of acceleration due to gravity at the latitude 45° on the earth becomes zero if the angular velocity of rotation of earth is

Answer 1

The outward centrifugal force due to rotation of earth decreases the net gravitational force. We know that the net acceleration due to gravity is given by the relation:

g' = g - ω²Rcos²Ф

where g = normal acceleration due to gravity = 9.8 m/s²

R = radius of the earth = 6371000 m

Ф = inclination of the object = 45°

Hence for g' = 0

g = ω²Rcos²Ф

=> 9.8 = ω² x 6371000 x 1/2

=> ω² = 19.6/6371000

=> ω = 0.0017 rotation per second

= 0.0017 x 60 rpm

= 0.102 rpm

Hence the apparent acceleration due to gravity of a body will become zero at 45° for an angular velocity of 0.102 rpm.