Question

A body is weighed by a spring balance to be 1.000 kg at the North Pole. How much will it weigh at the equator? Account for the earth's rotation only.

Answer 1

Let g_p be the acceleration due to gravity at the poles.
Let g_e be the acceleration due to gravity at the equator.

Now, acceleration due to gravity at the equator is given by
g_e = g_p $-$ ω²r
= 9.81 − (7.3 × 10⁻⁵)² × 6400 × 10³
= 9.81 − (53.29 × 10⁻¹⁰) × 64 × 10⁵
= 9.81 − 0.034 = 9.776 m/s²
Now, mg_e = 1 kg × 9.776 m/s²
= 9.776 N
∴ The body will weigh 9.776 N at the equator.