Question

The escape velocity from the earth is $11.2km/sec$. The escape velocity from a planet having twice the radius and the same mean density as the earth, is

• A. $11.2km/sec$
• B. $22.4km/sec$
• C. $15.00km/sec$
• D. $5.8km/sec$

Answer 1

Answer: (B)

$22.4km/sec$

For escape velocity the formula is,
$v_e=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2G\frac{4}{3}\pi R^3\rho }{R}}$
[$\rho$ is density of the planet, $R$ is radius.]
$=\sqrt{\frac{8}{3}G\pi R^2\rho }$
$v_e=R\sqrt{\frac{8}{3}G\pi \rho }$
$v_e\propto R$
If radius becomes twice, $v_e$ will also become twice. So new escape velocity$=2\times 11.2=22.4km/sec$