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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 which the Earth would have to rotate about its axis so that the person at the equator will weigh $\frac{3}{4} W$ . Radius of the Earth is $6400 km$ and $g = 10 m / s^{2}$ .

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$0.83 \times 10^{- 3} r a d / s$

$0.63 \times 10^{- 3} r a d / s$

$0.28 \times 10^{- 3} r a d / s$

$1.1 \times 10^{- 3} r a d / s$

answer is A.

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Detailed Solution

Here, the weight of person on the equator $= W$ .

If Earth rotates about its axis, then weight $= \frac{3 W}{4}$

Radius of the Earth $= 6400 km$

The acceleration due to gravity at the equator, $g_{e} = g - ω^{2} R \cos^{2} θ$

$\frac{3}{4} g = g - ω^{2} R \cos^{2} 0 ° or ω^{2} R = \frac{g}{4} ω = \sqrt{\frac{g}{4 R}} = \sqrt{\frac{10}{4 \times 6400 \times 10^{3}}} = 0.63 \times 10^{- 3} rad / s$

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