The condition for a uniform spherical mass m | vedclass

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Question

(C) For an object to become a black hole,its escape velocity must be equal to or greater than the speed of light $(c)$.The escape velocity $v_e$ from

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) For an object to become a black hole,its escape velocity must be equal to or greater than the speed of light $(c)$.The escape velocity $v_e$ from the surface of a spherical mass $m$ of radius $r$ is given by the formula:$v_e = \sqrt{\frac{2Gm}{r}}$For the object to be a black hole,the condition is $v_e \ge c$.Substituting the expression for $v_e$,we get:$\sqrt{\frac{2Gm}{r}} \ge c$Therefore,the correct option is $C$.

The condition for a uniform spherical mass $m$ of radius $r$ to be a black hole is [$G$ = gravitational constant and $c$ = speed of light].

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