Question
What is the angular velocity at any point on the equator so that the body feels weightlessness?
✓
Answer
At any point on the surface of earth, the acceleration due to gravity is, $\text{g}'=\text{g}\Big(1-\frac{\text{R}\omega^2}{\text{g}}\cos^2\alpha\Big),$ where $\alpha$ is the latitude. For equator, $\alpha=0$ To feel weightlessness $\text{g}'=0$ $\therefore\text{g}\Big(1-\frac{\text{R}\omega^2}{\text{g}}\Big)=0$ $\therefore\omega=\sqrt{\frac{\text{g}}{\text{R}}}$
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