Question

A body weighs 98N on a spring balance at the north pole . What will be its weight recorded on the same scale if it shifted to the equator? Use GM/R^2 = 9.8 m/s and the radius of the earth is R=6400km

Answer 1

use the eqn g'=g-Rw^2cos (theta), where theta is the angle of any point of earth made with equator and w is the angular velocity in rad/s

since north pole is inclined at 90 degrees to equator, u have g'=g ie acceleration at north pole is purely g(no contribution of angular velocity)

so mg=98 N at north pole.

so m=98/9.8=10 kg.

now calculate effective g at equator g'= g-r*w^2(since cos theta=1 since theta is zero)

=9.8-(6400*10^3*((2*pi/24 hours)radian)^2=9.799 m/s^2

mg'= 9.799*10=97.99 N

cheers. i am a physics prof and u can ask me more doubts.