Question

The rotation of the Earth having radius $R$ about its axis speeds 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 C $\pi \sqrt{\frac{R}{g}}$

$0=g-{Rw}^2{\cos }^{2}60°w^2=\frac{4g}{R}or,w^2=2\sqrt{\frac{g}{R}}\frac{2\pi }{T}=2\sqrt{\frac{g}{R}}\therefore T=\pi \sqrt{\frac{R}{g}}$