Question

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

• A. 1
• B. 8.5
• C. 17
• D. 34

Answer 1

The Correct Option is C

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.