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(C) For an object to become a black hole,its escape velocity must be equal to the speed of light $(c)$.The formula for escape velocity is $v_{esc} = \

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$10^{-2} \, m$

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(C) For an object to become a black hole,its escape velocity must be equal to the speed of light $(c)$.The formula for escape velocity is $v_{esc} = \sqrt{\frac{2GM}{R}}$.Setting $v_{esc} = c$,we get $c = \sqrt{\frac{2GM}{R}}$,which implies $R = \frac{2GM}{c^2}$.Given $G = 6.67 	imes 10^{-11} \, N \cdot m^2/kg^2$,$M = 5.98 	imes 10^{24} \, kg$,and $c = 3 	imes 10^8 \, m/s$:$R = \frac{2 	imes 6.67 	imes 10^{-11} 	imes 5.98 	imes 10^{24}}{(3 	imes 10^8)^2}$$R = \frac{79.77 	imes 10^{13}}{9 	imes 10^{16}}$$R \approx 8.86 	imes 10^{-3} \, m \approx 10^{-2} \, m$.

$A$ 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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