A plumb bob does not hang exactly along a line directed to the center of the Earth's rotation. How much does the plumb bob deviate from a radial line at 38.5° north latitude? Assume that the Earth is spherical

Answer 1

The string must apply a centripetal acceleration perpendicular to the earth's axis, equal to R cos 38.5 w^2. w is the angular velocity of the Earth's rotation in radians per second, 7.27*10^-5 rad/s, and R is the radius of the earth, 6357*10^3 m. That makes the centripetal acceleration a = 3.36*10-2 m/s^2

The plum bob's deviation angle (in radians) is
theta = a sin 38.5/g

The sin of the latitude enters in because you have to take the component of the centripetal force perpendicular to the string