Question

Believe it or not, a plumb-bob does not hang exactly along a line directed to the centre of the Earth! Determine how far off true plumb a bob hangs in Cape Town. In which direction is the deviation (north, east, south, or west)? How would your answer differ for a plumb-bob in London? (Assume that the Earth is spherical.)

Answer 1

What is centripetal acceleration as a function of latitude?

w = 2 pi/24 hours = 2 pi /(24*3600) rad/s

Ac = w^2 r
r = Re cos (Lat)
where Re is earth radius and Lat is latitude angle

calculate Ac
call tension in plumb bob line T
then T will be off the direction to center of earth by angle A

T vector - mg vector = m Ac vector
draw those with mg toward earth center and Ac horizontal toward earth N-S axis

Then |T| cos A = m |Ac| cos Latitude +mg
and |T| sin A = m |Ac| sin Latitude

approximate |T| by m g
then sin A = (Ac/g) sin Latitude approximately

Answer 2

4.7 degrees