Question

A black hole is a body from whose surface nothing ever escape. What is the condition for a uniform spherical mass m to be a black hole? What should be the radius of such a black hole if its mass is the same as that of earth?

Answer 1

From Einstein’s special theory of relativity, we know that the speed of light, c = (3 x 10⁸ ms⁻¹ ) cannot be exceeded by any moving particle. Thus c is the upper limit to the projectile escape speed.

i.e., v_e = \(\big(\frac{2GM}{R}\big)^{\frac{1}{2}}\leq e\)

if M = M_e

then R = \(\frac{2GMe}{c^2}\) 

= \(\frac{2\times(6.67\times10^{-11})\times(6\times10^{24)}}{(3\times10^8)^2}\)

= 8.9 x 10^-3 m = 1 cm

It means the earth can act as a black hole. If it shrinks to a very small size of nearby 1 cm radius, which is the size of a berry.