Gravitation Question 211

Question: The condition for a uniform spherical mass m of radius r to be a black hole is [G= gravitational constant and g= acceleration due to gravity][AIIMS 2005]

Options:

A) $ [{{(2Gm/r)}^{1/2}}\le c] $

B) $ [{{(2Gm/r)}^{1/2}}=c] $

C) $ [{{(2Gm/r)}^{1/2}}\ge c] $

D) $ [{{(gm/r)}^{1/2}}\ge c] $

Show Answer

Answer:

Correct Answer: C

Solution:

Escape velocity for that body $ [v_{e}=\sqrt{\frac{2Gm}{r}}] $

$ [v_{e}] $ should be more than or equal to speed of light i.e.

$ [\sqrt{\frac{2Gm}{r}}\ge c] $



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