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 $\omega =\frac{2\pi }{T}=\frac{2\pi }{24\times 60\times 60}rad{s}^{-1}$ At equator, $g^{\prime }=g-R_e{\omega }^{\prime 2}$ or $=g-R_e{\omega }^{\prime 2}$ or ${\omega }^{\prime }=\sqrt{{\frac{g}{R}}_e}=\frac{2\pi }{84.6\times 60}$ = $\frac{{\omega }^{\prime }}{\omega }=\frac{24\times 60\times 60}{84.6\times 60}=17$ $\Rightarrow {\omega }^{\prime }=17\omega$ So, value of x is 17.