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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 $\times 10^{24} kg)$ have to be compressed to be a black hole?

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$10^{- 9} m$

$10^{- 6} m$

$10^{- 2} m$

100 m

answer is C.

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Detailed Solution

$V_{e} = \sqrt{\frac{2 GM}{R}} = C$

R = $\frac{2 GM}{C^{2}} = \frac{2 \times 6.67 \times 10^{- 11} \times 5.98 \times 10^{24}}{{(3 \times 10^{8})}^{2}}$

= $\frac{2 \times 6.67 \times 5.98}{9} \times 10^{- 3} m$

= $8.86 \times 10^{- 3} = 10^{- 2} m$

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