A black hole is an object whose gravitational field is so strong that… | NEET 2014 (AIPMT)

Q69NEET 2014 · AIPMTMedium

Escape Velocity

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 $\times$ 1024 kg) have to be compressed to be a black hole?

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Answer: (c)

Black hole: escape speed equals $c$ , so $\sqrt{\frac{2GM}{R}} = c \Rightarrow R = \frac{2GM}{c^2}$ .
$R = \frac{2\times 6.67\times10^{-11}\times 5.98\times10^{24}}{(3\times10^{8})^2} = \frac{7.98\times10^{14}}{9\times10^{16}}$ .
$R \approx 8.9\times10^{-3}\text{ m} \approx 10^{-2}\text{ m}$ .
So the answer is (c) $10^{-2}$ m.

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