Q112 / 180 · AIIMS 2005 · Physics

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
    $\left(\frac{2 G m}{r}\right)^{1 / 2} \leq c$
  • B
    $\left(\frac{2 g m}{r}\right)^{1 / 2}=c$
  • Correct answer
    C
    $\left(\frac{2 G m}{r}\right)^{1 / 2} \geq c$
  • D
    $\left(\frac{g m}{r}\right)^{1 / 2} \geq c$

Solution

The criterion for a star to be black hole is $$ \frac{G M}{c^2 R} \geq \frac{1}{2} \text { or, } \sqrt{\frac{2 G M}{R}} \geq c . $$

Hence, the correct answer is option: 'C'.

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