What should be angular speed with which earth have to rotate on its axis so that a person on equator

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7.Gravitation

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What should be the angular speed with which the earth have to rotate on its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as present?

A

$\sqrt{\frac{2 g}{5 R}}$

B

$\sqrt{\frac{2 R}{5 g}}$

C

$\frac{2 \sqrt{R}}{\sqrt{5 g}}$

D

$\frac{2 g}{5 R}$

Solution

(a)

$w=w-m \omega^2 R$

$\Rightarrow m g_e=m g-m \omega^2 R$

$m g_e=\frac{3}{5} m g$

$\Rightarrow m \omega^2 R=\frac{2}{5} m g$

$\Rightarrow \omega=\sqrt{\frac{2 g}{5 R}}$

Standard 11

Physics

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