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

Answer: (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.