Question

The angular velocity of the earth about its polar axis so that the weight of the body at the equator will be zero is

• A. 1.25 x ${10}^{-3}rad{s}^{-1}$
• B. 2 $rad{s}^{-1}$
• C. 1 $rad{s}^{-1}$
• D. 0

Answer 1

Answer: (A)

1.25 x ${10}^{-3}rad{s}^{-1}$

$g^{\prime }=g-{\omega }^{2}R{\cos }^2\varphi$

At equator, $g^{\prime }=g-{\omega }^{2}R$

For weight to be zero, $g^{\prime }=0$

$\Rightarrow {\omega }^{2}R=g$

$={\omega }^2=\frac{g}{R}=\frac{9.8}{6400\times {10}^5}=\frac{9.8}{6.4}\times {10}^{-6}$

$\Rightarrow \omega =1.25\times {10}^{-3}rad{s}^{-1}$