Question

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?

I got my answer to be 0.122288439 deg but it was incorrect. I used theta= a(sin 38.5)/g (which produces an answer in radians and I converted to degrees)Please & thank you!

Answer 1

You may have used a wrong value for a, the centripetal acceleration at the equator. Also, there should be a cosine of latitude, not sine, in the formula. There is no rotation effect at the poles, where your formula woulde say it it a maximum.

a = R w^2, where R is the radius of the earth and w is the angular rotation rate in rad/s.
Approximate values are:
R = 6.4*10^6 m
w = 7.27*10^-5 rad/s
a = Rw^2 = 3.4*10^-2 m/s^2
a/g*cos 38.5 = 2.8*10^-3 radians
= 0.16 degrees

You also have to many significant figures in your answer.