Question

A mass $6\times {10}^{24}$ kg(mass of earth) is to be compressed in a sphere in such a way that the escape velocity from its surface $3\times {10}^8\frac{m}{s}$. The radius of the sphere should be mm.

Answer 1

The mass of the sphere = $6\times {10}^{24}$ kg

Escape velocity = 3$\times {10}^8\frac{m}{s}$

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

or R = $\frac{2GM}{V_c^2}$

$=\frac{2\times 6.67\times {10}^{-11}\times 6\times {10}^{24}}{{(3\times {10}^8)}^2}=\frac{80.02}{9}\times {10}^{-3}=8.89\times {10}^{-3}m\approx 9mm$