Question

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

• A. $9\text{mm}$
• B. $8\text{mm}$
• C. $7\text{mm}$
• D. $6\text{mm}$

Answer 1

The correct option is A $9\text{mm}$

Escape velocity is given by,
$${\text{v}}_e=\sqrt{\frac{2GM}{R}}$$
$\Rightarrow R=\frac{2GM}{{\text{v}}_e^2}$
$\Rightarrow R=\frac{2\times 6.67\times {10}^{-11}\times 6\times {10}^{24}}{(3\times {10}^8{)}^2}$
$\Rightarrow R\approx 9\times {10}^{-3}\text{m}$
$\Rightarrow R\approx 9\text{mm}$