Question

The radius in kilometers, to which the present radius of the earth ($R$ $=6400$ km) is to be compressed so that the escape velocity is increased ten times is(in kms) :

• A. 6.4
• B. 64
• C. 640
• D. 4800

Answer 1

The correct option is B 64

Escape speed is, $v=\sqrt{\frac{2GM}{R}}$
Assuming the mass of earth is constant while compressing the radius.
$v^{\prime }=10v$
$\Rightarrow \sqrt{\frac{2GM}{R^{\prime }}}=10\times \sqrt{\frac{2GM}{R}}$
$\Rightarrow \sqrt{R^{\prime }}=\frac{\sqrt{R}}{10}\Rightarrow R^{\prime }=\frac{1}{100}\times 6400=64$ $km$