Question

Escape velocity from Earth is about 11 km/s. The escape velocity from a planet, 4 times the size of the Earth with same mean density is

• A. 44 km/s
• B. 22 km/s
• C. 16.5 km/s
• D. 88 km/s

Answer 1

Answer: (A)

Escape velocity of a planet
$v=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2G\times \frac{4}{3}\pi R^3\times \rho }{R}}$
$v=R\sqrt{\frac{8\pi }{3}G\rho }$
For same $\rho ,v\propto R$
$\therefore \frac{v_E}{v_P}=\frac{R_E}{R_P}$
Here, $v_E=11Km{s}^{-1},R_E=R,R_p=4R,v_P=?$
$\therefore \frac{11}{v_P}=\frac{R}{4R}$
or, $v_P=44km{s}^{-1}$