Question

If the apparent weight of the bodies at the equator is to be zero, then the earth should rotate with angular velocity:

• A. $\sqrt{\frac{g}{R}}$ rad/s
• B. $\sqrt{\frac{2g}{R}}$ rad/s
• C. $\sqrt{\frac{g}{2R}}$ rad/s
• D. $\sqrt{\frac{3g}{2R}}$ rad/s

Answer 1

The correct option is A $\sqrt{\frac{g}{R}}$ rad/s

For a body of mass $m$ to go weightless at the equator:

$mg-m{\omega }^{2}R=0$

or, $mg=m{\omega }^{2}R$

or, $\omega =\sqrt{\frac{g}{R}}$