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A box weighs 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to. (Take g = 10 ms⁻² at the north pole and the radius of the earth = 6400 km)

1. 194.32 N
2. 195.66 N
3. 195.32 N
4. 194.66 N

Correct answer: 195.32 N

Solution

m = 196/10 = 19.6 kg. omega = 2pi/86400 = 7.27e-5 rad/s, so omega^2*R = (7.27e-5)^2 x 6.4e6 = 0.0338 m/s^2. Loss = m*omega^2*R = 19.6 x 0.0338 = 0.66 N, giving weight 196 - 0.66 ~ 195.32 N.

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