Q. The angular velocity of rotation of star (of mass $M$ and radius $R$) at which the matter start to escape from its equator will be
A) $\sqrt{\frac{2GM^{2}}{R}}$
B) $\sqrt{\frac{2GM}{g}}$
C) $\sqrt{\frac{2GM}{R^{3}}}$
D) $\sqrt{\frac{2GR}{M}}$
Explanation
(c) Escape velocity $v = \sqrt{\frac{2GM}{R}}$
If star rotates with angular velocity $\omega$
Then $\omega = \frac{v}{R} = \frac{1}{R}\sqrt{\frac{2GM}{R}} = \sqrt{\frac{2GM}{R^{3}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.