Question

With what angular velocity the earth should spin in order that a body lying at ${30}^o$ latitude becomes weightless?

• A. $\sqrt{\frac{2g}{3R}}$
• B. $\sqrt{\frac{4g}{R}}$
• C. $\sqrt{\frac{g}{3R}}$
• D. $\sqrt{\frac{4g}{3R}}$

Answer 1

The correct option is D $\sqrt{\frac{4g}{3R}}$

the apparent weight of a person on the Lattitude at

$\alpha$= 30

$W^{\prime }=W-m{R}_e{cos}^2\alpha \times {\omega }^2$

$g^{\prime }=g-R\frac{3}{4}\times {\omega }^2$

$g^{\prime }=0$

$\omega =\sqrt{\frac{4g}{3R}}$