Using a spring balance, a body is found to weigh 1.000 kg at the north pole. Determine its weight at the equator, considering only the effect of the earth's rotation.

Step-by-step solution

The weight of the body at the north pole is given by W_p = mg = 1.000 kg . At the equator, the effective acceleration due to gravity is reduced by the centrifugal acceleration due to the Earth's rotation. The effective gravity is g' = g - R ^2 . The weight at the equator is W_e = m(g - R ^2) = mg (1 - R ^2 g ) = W_p (1 - R ^2 g ) . Substituting the known standard values: Radius of Earth, R = 6.4 10^6 m Angular velocity of Earth, = 2 T = 2 24 3600 7.27 10⁻⁵ rad/s Acceleration due to gravity, g = 9.8 m/s ^2 Calculati