Question

$V_e,V_p$ denotes the escape velocity from the earth and another planet having twice the density as the earth, Then

• A. $V_e=V_p$
• B. $V_e=V_p/\sqrt{2}$
• C. $V_e=2V_p$
• D. $V_e=V_p/4$

Answer 1

The correct option is B $V_e=V_p/\sqrt{2}$

$Mass=density\times volume$

$M=\rho V$

Escape velocity

$v_e=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2G\rho V}{R}}=\sqrt{\rho }\sqrt{\frac{2G\rho V}{R}}$

$v_e\alpha \sqrt{\rho }$

G= Gravitational Constants

$R$ = Mass of the planet

$\rho$ =density of planet

$V$ = volume of planet

$\frac{V_e}{V_p}=\frac{\sqrt{{\rho }_e}}{{\sqrt{\rho }}_p}=\frac{\sqrt{{\rho }_e}}{\sqrt{2{\rho }_e}}$

$V_e=\frac{V_p}{\sqrt{2}}$

Hence, the relation between escape velocity $V_e=\frac{V_p}{\sqrt{2}}$