Question

The escape velocity from earth is 11 km/sec. The escape velocity from a planet having equal density and double radius of the earth is:-

• A. 15.56 km/sec
• B. 22 km/sec
• C. 5.5 km/sec
• D. 11 km/sec

Answer 1

The correct option is B 22 km/sec

$\rho$ is given by $\rho =\frac{M}{\frac{4}{3}\pi R_e^3}$

$=>M=\rho \times \frac{4}{3}\pi R_e^3$

also escape velocity is given by $V=\sqrt{\frac{2GM}{R_e}}$

so $v=\sqrt{\frac{2G\rho \pi R_e^3}{3R_e}}$

so $V$ is directly proportional to $R_e$ if $\rho$ is constant.

so if radius is doubles then escape velocity will also be doubled. i.e. $11\times 2=22$

so answer is option B.