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 m a s s = 5.98 × 10 24 k g have to be compressed to be a

Question

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 m a s s = 5.98 × 10 24 k g have to be compressed to be a black hole?

TestHub · Accepted Answer

According to question the light is unable to escape the gravitational pull of the black hole thus the escape velocity is equal to the speed of the light so,
Escape velocity is $V_{e} = C$ .
We know that escape velocity is given by,

$\sqrt{\frac{2 G M}{R}} = 3 \times 10^{8}$

Putting in the values we get,
$\Rightarrow \sqrt{\frac{2 \times (\frac{20}{3} \times 10^{- 11}) (6 \times 10^{24})}{R}} = 3 \times 10^{8}$

Thus, on solving we get,
$R \approx 9 m m \approx 10^{- 2} m$

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