If the Earth has no rotational motion, the weight of a person on the equator is W . Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will

Question

If the Earth has no rotational motion, the weight of a person on the equator is W . Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3 4 W . The radius of the Earth is 6400 km and g = 10 m s - 2

TestHub · Accepted Answer

Due to the rotation of the earth,

Changed gravitational acceleration, $g^{'} = g - ω^{2} R \cos^{2} θ$

At the equator, angle of inclination, $θ = 0$

$\frac{3 g}{4} = g - ω^{2} R$

$w^{2} R = \frac{g}{4}$

$w = \sqrt{\frac{g}{4 R}}$

$= \sqrt{\frac{10}{4 \times 6400 \times 10^{3}}}$

$= \frac{1}{2 \times 8 \times 100}$

$= \frac{1}{1600} = \frac{1}{16} \times 10^{- 2} = 0.6 \times 10^{- 3} rad s^{- 1}$ .

Physics - Gravitation Question with Solution | TestHub

Options:

Doubts & Discussion