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Q.

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]

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a

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

b

${(gm / r)}^{1 / 2} \geq c$

c

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

d

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

answer is C.

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Detailed Solution

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

v_e should be more than or equal to speed of light

i.e. $\sqrt{\frac{2 Gm}{r}} \geq c$

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