The angular velocity of rotation of star (

Your Ultimate Guide to JEE & NEET Question Solutions

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{{2G{M^2}}}{R}} $

B

$\sqrt {\frac{{2GM}}{g}} $

C

$\sqrt {\frac{{2GM}}{{{R^3}}}} $

D

$\sqrt {\frac{{2GR}}{M}} $

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

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}}}} $