Question

The angular velocity of earth's rotation about its axis is $'\omega'.$ An object weighed by a spring balance gives the same reading at the eiquator as at a height 'h' above the poles. The value o f 'h' will be

• A. $\frac{\omega^2\,R^2}{g}$
• B. $\frac{\omega^2\,R^2}{2g}$
• C. $\frac{2\omega^2\,R^2}{g}$
• D. $\frac{2\omega^2\,R^2}{3g}$

Answer 1

The Correct Option is B

$mg - m \omega^2R = mg \left( 1 - \frac{2h}{R} \right)$ $\Rightarrow \, \omega^2 R =\frac{2gh}{R} \, \Rightarrow \, h =\frac{\omega^2R^2}{2g}$