Question

The angular velocity of rotation of a star (of mass $M$ and radius $R$) at which the matter starts to escape from its equator, is

• A. $\sqrt{\frac{2GM}{R}}$
• B. $\sqrt{\frac{2GR}{M}}$
• C. $\sqrt{\frac{2GM^{2}}{R}}$
• D. $\sqrt{\frac{2GM}{R^{3}}}$

Answer 1

Answer: (D)

Given: Mass of star = M and radius of the star = R. We know that escape angular velocity of the star
$\left(\omega_{e}\right)=\frac{v_{e}}{R}=\frac{1}{R}\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2GM}{R^{3}}}.$
(where escape velocity $(v_{e} = \sqrt{\frac{2GM}{R}})$