Question

The escape velocity from the earth is $11km/sec$. The escape velocity from a planet having twice the radius and same density as earth is :

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

Answer 1

The correct option is A $22km/sec$

Escape speed is $v_e=\sqrt{\frac{2GM}{R}}$
If we express $Mass$ in terms of $Volume$ and $Density$, $v_e$ in terms of density can be written as,
$v_e=2R\sqrt{\frac{2G\pi \rho }{3}}=11km/s$; on Earth's surface.
For another planet, radius is twice that of Earth but density is same.
$\therefore v_e^{{}^{\prime }}=2\left(2R\right)\sqrt{\frac{2G\pi \rho }{3}}=2\times 11=22$ km/s