Question

A mass of $6\times {10}^{24}$ kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape elocity from its surface is $3\times {10}^8$ m $s^{-1}$ What should be the radius of the sphere?

Answer 1

The mass of the sphere $=6\times {10}^{24}$ kg Escape velocity = $3\times {10}^8$
$Ve=\frac{2GM}{R}orR=\frac{2GM}{V{e}^2}=\frac{2\times 6.67\times {10}^{-11}\times 6\times {10}^{24}}{(3\times {10}^8{)}^2}=\frac{2\times 40.02\times {10}^{13}}{9\times {10}^{16}}=\frac{80.02}{9}\times {10}^{-3}m=8.89\times {10}^{-3}m=9mm.$