Q. What should be the angular velocity of earth so that a body on its equator is weightless?
A) $\frac{1}{8000}$ rad $s^{- 1}$
B) $\frac{1}{8}rad\ s^{- 1}$
C) $\frac{1}{800}rad\ s^{- 1}$
D) $\frac{1}{80}rad\ s^{- 1}$
Explanation
(c) For weightlessness state of a body on equator
$mg = mR\omega^{2}$
or $\omega = \sqrt{\frac{g}{R}} = \sqrt{\frac{10}{6400 \times 100}} = \frac{1}{800}$ rad$s^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.