Question

If the escape velocity from the surface of a spherical planet is given by $2\sqrt{\frac{GM}{K}}$, where $M$ is the mass of the planet and $K$ is a constant, then the radius of the planet is

• A. $\frac{K}{2}$
• B. $K$
• C. $2K$
• D. $4K$

Answer 1

Answer: (A)

$\frac{K}{2}$

Escape velocity of planet with radius $R,v_e=\sqrt{\frac{2GM}{R}}$
given, $v_e=2\sqrt{\frac{GM}{K}}$
So, $v_e=2\sqrt{\frac{GM}{K}}=\sqrt{\frac{2GM}{R}}$ and solving it we get
$R=\frac{K}{2}$