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 kg) have to be compressed to be a black hole? [2014]

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Solution

Q.
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 [2014]

1 $10^{- 9}$ m

2 $10^{- 6}$ m

3 $10^{- 2}$ m

4 100 m

Ans.
(3)

Light cannot escape from a black hole,

$v_{e} = c \Rightarrow \sqrt{\frac{2 G M}{R}} = c or R = \frac{2 G M}{c^{2}}$

$R = \frac{2 \times 6.67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2} \times 5.98 \times 10^{24} kg}{{(3 \times 10^{8} ms^{- 1})}^{2}}$

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

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