Gravitation

JEE Main level, single correct, medium

94 of 223

Question 94 of 223

If the Earth has no rotational motion, the weight of a person on the equator is WW. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 34W\dfrac{3}{4}W. The radius of the Earth is 6400km6400km and g=10ms−2g=10m{s}^{-2}

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Answer: (A) 0.63×10−3rads−10.63\times {10}^{-3}rad{s}^{-1}

Due to the rotation of the earth,

Changed gravitational acceleration, g′=g−ω2Rcos⁡2⁡θ{g}^{'}=g-{\omega }^{2}R{\cos }^{2}⁡\theta

At the equator, angle of inclination, θ=0\theta =0

3g4=g−ω2R\dfrac{3g}{4}=g-{\omega }^{2}R

w2R=g4{w}^{2}R=\dfrac{g}{4}

w=g4Rw=\sqrt{\dfrac{g}{4R}}

=104×6400×103=\sqrt{\dfrac{10}{4\times 6400\times {10}^{3}}}

=12×8×100=\dfrac{1}{2\times 8\times 100}

=11600=116×10−2=0.6×10−3rads−1=\dfrac{1}{1600}=\dfrac{1}{16}\times {10}^{-2}=0.6\times {10}^{-3}rad{s}^{-1}.

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