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].

• A. ${\left(\frac{2Gm}{r}\right)}^{1/2}\le c$
• B. ${\left(\frac{2gm}{r}\right)}^{1/2}=c$
• C. ${\left(\frac{2Gm}{r}\right)}^{1/2}\ge c$
• D. ${\left(\frac{gm}{r}\right)}^{1/2}\ge c$

Answer 1

The correct option is C ${\left(\frac{2Gm}{r}\right)}^{1/2}\ge c$

A black hole does not allow light to escape its surface. In other words for a black hole body escape velocity becomes $>$ velocity of light.
Now for a body of mass $m$,
Escape velocity $={\left(\frac{2Gm}{r}\right)}^{1/2}$
So, $={\left(\frac{2Gm}{r}\right)}^{1/2}\ge c$