Question

How much should the Earth be compressed without losing any material in order for it to become a blackhole.

Answer 1

solution:-

in order for earth to became a blackhole without losing any mass its escape velocity should be at least equal to speed of light.

$\sqrt{\frac{2GM_e}{R}}=c$

where G=gravitation constant$(6.67\times10^{-11}Nm^2/kg^2)$

mass of earth $M_e=5.9\times10^{24}kg$

speed of light$(c)=3\times10^8m/s$

then radius of earth should be after compressed

$R=\frac{2GM_e}{c^2}$

by putting the value of G,M_e and c

$R=\frac{2\times6.67\times10^{-11}\times5.98\times10^{24}}{9\times10^{16}}$

$R=0.886\times10^{-2}m$

$\fcolorbox{green}{yellow}{$R≈10^{-2}m$}$

therefore radius of earth should be 1 cm to became a blackhole.