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. $100m$

Answer 1

The correct option is C ${10}^{-2}$ m

For earth to be black hole the escape velocity should be at least equal to speed of light.

$\therefore$ escape velocity $=$ speed of light

$\sqrt{\frac{2GM}{R}}=C$

$R=\frac{2GM}{C^2}$

$R=\frac{2\times 6.67\times {10}^{-11}\times 5.98\times {10}^{24}}{9\times {10}^{16}}=8.86\times {10}^{-3}m={10}^{-2}m$