Due to the Earth’s rotation and oblate spheroidal shape, the acceleration of gra

Question

Due to the Earth’s rotation and oblate spheroidal shape, the acceleration of gravity on Earth varies as a function of latitude from gpoles = 9.832 m s 2 at the North and South Poles to gequator = 9.780 m s 2 at the equator.

Find, (a) the ratio of the period of a single oscillation at the poles Tpoles to that of a single oscillation at the equator Tequator first algebraically then numerically

(b) for a pendulum with length l = 2.500m, calculate Tpoles and Tequator

(c) to what precision would one need to measure Tpoles and Tequator to calculate a difference in g?

Explanation / Answer

we know, T = 2*pi*sqrt(L/g)

a) T_poles/T_equator = sqrt(g_equator/g_poles)

= sqrt(9.78/9.832)

= 0.9974

b) T_poles/T_equator = sqrt(g_equator/g_poles)

= 0.9974

The ratio does not depend on the legth of the pendulum.

c) we need to take 4 dignificant figures

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