Question

The escape velocity for earth is v. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

• A. $\frac{v}{3}$
• B. $\frac{2v}{3}$
• C. $\frac{3v}{4}$
• D. $\frac{9v}{4}$

Answer 1

Answer: (C)

$\frac{3v}{4}$

Answer 2

Escape velocity ($v_e$) is given by $v_e = \sqrt{\frac{2GM}{R}}$, where G is the gravitational constant, M is the mass of the planet, and R is the radius.

For the new planet, $M' = 9M$ and $R' = 16R$.

$v_e' = \sqrt{\frac{2G(9M)}{16R}} = \frac{3}{4}\sqrt{\frac{2GM}{R}} = \frac{3}{4}v_e$