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

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 &#160; W . The radius of the Earth is 6400 &#160; km and g = 10 &#160; m &#160; s - 2

Aicharya · 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}

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If the Earth has no rotational motion, the weight of a person on the equator is W . Determine the speed with…

Solution