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 (mass $= 5.98 \times 10^{24} \, kg$) have to be compressed to be a black hole?

• A. $10^{-9} \, m$
• B. $10^{-6} \, m$
• C. $10^{-2} \, m$
• D. $100\, m$

Answer 1

Answer: (C)

Light cannot escape from a black hole,
$v_{\text{esc }}=c$
$\sqrt{\frac{2 G M}{R}}=c $
or $ R=\frac{2 G M}{c^{2}}$
$R=\frac{2 \times 6.67 \times 10^{-11} N m ^{2} kg ^{-2} \times 5.98 \times 10^{24} kg }{\left(3 \times 10^{8} m s ^{-1}\right)^{2}}$
$=8.86 \times 10^{-3} m \approx 10^{-2} m$