Question

The correct relation between escape velocity $v_e$ and critical velocity $v_0$ is :

• A. $v_e=\sqrt{\frac{3}{2}}{v}_0$
• B. $v_e=\sqrt{2}{v}_0$
• C. $v_e=\sqrt{3}{v}_0$
• D. $v_e=\sqrt{\frac{2}{3}}{v}_0$

Answer 1

The correct option is B $v_e=\sqrt{2}{v}_0$

The critical velocity or orbital velocity of a satellite of planet of radius $R$ is given by ,

$v_o=\sqrt{gR}$ ..................eq1

The escape velocity on a planet of radius $R$ is given by ,

$v_e=\sqrt{2gR}$ ..................eq2

dividing eq2 by eq1 , we get

$\frac{v_e}{v_o}=\frac{\sqrt{2gR}}{\sqrt{gR}}=\sqrt{2}$

or $v_e=\sqrt{2}{v}_o$