Question

17. The escape speed for a planet is vo. What is the
escape speed corresponding to another planet of
twice the radius and half the density?​

Answer 1

Escape velocity is directly proportional to the square root of mass of planet

and Escape velocity is indirectly proportional to the Distance from the centre of mass that is radius.

Hence,

$mass \: becomes \: half = \sqrt{ \frac{M}{2} } \\ radius \: becomes \: twice = \sqrt{ \frac{1}{2 \times r} }$

Don't consider the M and r in above two and multipy we get 1/2

Hence the escape speed becomes half.