Gravitation Question 154

Question: 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[MH CET 1999]

Options:

A) $ [\sqrt{\frac{2GM^{2}}{R}}] $

B) $ [\sqrt{\frac{2GM}{g}}] $

C) $ [\sqrt{\frac{2GM}{R^{3}}}] $

D) $ [\sqrt{\frac{2GR}{M}}] $

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Answer:

Correct Answer: C

Solution:

Escape velocity $ [v=\sqrt{\frac{2GM}{R}}] $

If star rotates with angular velocity w then

$ [\omega =\frac{v}{R}=\frac{1}{R}\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2GM}{R^{3}}}] $



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