What should be angular speed of earth, so that a body lying on equator may appear weightlessnes

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7.Gravitation

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What should be the angular speed of the earth, so that a body lying on the equator may appear weightlessness $(g = 10\,m/s^2, R = 6400\,km)$

A

$\frac{1}{{800}}\,rad/s$

B

$\frac{1}{{400}}\,rad/s$

C

$\frac{1}{{600}}\,rad/s$

D

$\frac{1}{{100}}\,rad/s$

Solution

$\mathrm{g}_{\theta}=\mathrm{g}-\omega^{2} \mathrm{R} \cos ^{2} \theta$

at equator $\theta=0^{\circ} $ and for weight lessness

${g_{equator}}$ $=0$

$\Rightarrow 0=\mathrm{g}-\omega^{2} \mathrm{R} \cos ^{2} 0$

$\Rightarrow \omega=\sqrt{\frac{g}{R}}=\sqrt{\frac{10}{6400 \times 10^{3}}}=\frac{1}{800} \mathrm{\,rad} / \mathrm{sec}$

Standard 11

Physics

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