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Q.
The speed of earth’s rotation about its axis is $\omega$. Its speed is increased to $x$ times to make the effective acceleration due to gravity equal to zero at the equator. Then $x$ is
Earth rotates about its own axis in 24 h.
So, T = 24 x 60 x 60 s
So, angular speed of earth about its own axis
$\omega=\frac{2\pi}{T}=\frac{2\pi}{24\times60\times60}rad s^{-1}$
At equator, $g' = g - R_e\omega'^2$
or $=g - R_e\omega'^2$
or $\omega'=\sqrt{\frac{g}R_e}=\frac{2\pi}{84.6\times60}$
= $\frac{\omega'}{\omega}=\frac{24\times60\times60}{84.6\times60}=17$
$\Rightarrow \omega'=17\omega$
So, value of x is 17.