Question

The escape speed from the earth is about 11 km/s. The escape speed from a planet, having twice the radius and the same mean density as earth, is

• A. 22 km/s
• B. 11 km/s
• C. 5.5 km/s
• D. 15.5 km/s

Answer 1

The correct option is A 22 km/s

Escape velocity $v_{es}=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2G}{R}.\frac{4}{3}\pi R^3\rho }$

where $R$ is the radius of earth.
$v_{es}=\sqrt{\frac{8}{3}\pi G\rho R^2}=R\sqrt{\frac{8\pi G\rho }{3}}$

$⟹$ $v_{es}\propto R$
$\therefore \frac{{\left(v_{es}\right)}_{planet}}{{\left(v_{es}\right)}_{earth}}=\frac{2R}{R}=2$
$\Rightarrow {\left(v_{es}\right)}_{planet}=2\times {\left(v_{es}\right)}_{earth}$
$(v_{es}{)}_{planet}=2\times 11km/s=22km/s$