Question

The rotation of the Earth having radius R about its axis speed upto a value such that a man at latitude angle ${60}^o$ feels weightless. The duration of the day in such case will be.

• A. $8\pi \sqrt{\frac{R}{g}}$
• B. $8\pi \sqrt{\frac{g}{R}}$
• C. $\pi \sqrt{\frac{R}{g}}$
• D. $4\pi \sqrt{\frac{g}{R}}$

Answer 1

The correct option is A $8\pi \sqrt{\frac{R}{g}}$

For a man at an angle $\theta ={60}^o$

$T=2\pi \sqrt{\frac{R^3}{GM\left(\cos {60}^o\right)}}$

$2\pi \sqrt{\frac{R^2}{GM}\frac{R}{(\cos {60}^o}}$

$2\pi \sqrt{\frac{R}{g}\frac{1}{1/2}}$

$=8\pi \sqrt{\frac{R}{g}}$