Question

Block 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. $100m$

Answer 1

Answer: (C)

${10}^{-2}m$

Light is unable to escape so
$V_e=C$
$\sqrt{\frac{2GM}{R}}=3\times {10}^8$
$\Rightarrow \sqrt{\frac{2\times (\frac{20}{3}\times {10}^{-11})(6\times {10}^{24})}{R}}=3\times {10}^8$
get $R\approx 9mm\approx {10}^{-2}m$