# 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       W.  Radius of the Earth is 6400 km and g=10 m/s2. Option 1) 1.1×10−3 rad/s Option 2)  0.83×10−3 rad/s Option 3)  0.63×10−3 rad/s Option 4)  0.28×10−3 rad/s

As we learnt in

Variation in 'g' due to Rotation of earth -

$g'=g-\omega ^{2}R\cos ^{2}\lambda$

$\lambda \rightarrow$ latitude angle

$\omega \rightarrow$ Angular velocity of rotation of earth

$g' \rightarrow$ New value of 'g'.

- wherein

Apparent weight of body decrease with rotation of earth so value of g also decrease.

$g'= g-\omega^2R\cos ^2\theta \Rightarrow \frac{3g}{4}= g-\omega^2R$

At equator $\theta = 0$

$\frac{3}{4}g - g=\: \omega^2R$

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

$\omega^2R=\frac{g}{4R}\Rightarrow \omega=\sqrt{\frac{g}{4R}}=\sqrt{\frac{10}{4\times 6400\times 10^3}}$

$\omega^2= 0.6\times 10^-3 \:rad/sec$

Option 1)

Incorrect

Option 2)

Incorrect

Option 3)

Correct

Option 4)

Incorrect

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