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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?

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a

10^–9m

b

10^–6m

c

10^–2m

d

100 m

answer is C.

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Detailed Solution

As light can not escape from a black hole escape velocity from black hole $\geq$ velocity of light
$\begin{array}{l} \sqrt{\frac{2 GM}{R}} \geq C \\ \Rightarrow R \leq \frac{2 GM}{C^{2}} = \frac{2 \times 6.67 \times 10^{- 11} \times 5.98 \times 10^{24}}{9 \times 10^{16}} \\ \Rightarrow R \leq 8.8 \times 10^{- 3} m ≃ 10^{- 2} m \end{array}$

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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 =5.98×1024 kg have to be compressed to be a black hole?