Question

While approaching a planet circling a distant star, a space traveller

determines the planet’s radius to be half that of the Earth. After landing

on the surface he finds the acceleration due to gravity to be twice that

on the surface of the Earth. Find the ratio of the mass of the planet to

that of the Earth.

Answer 1

Let the mass of planet is Mp 
     radius of the planet is Rp 
                             use Gravitational concept,
 $\bold{g_p=\frac{GM_P}{R_P^2}}$------------(1)

similarly, mass of the esrth is Me
radius of the earth is Re,
then, $\bold{g_e=\frac{GM_e}{R_e^2}}$------------------(2)

        now, according to question,
 Rp = Re/2 and gp = 2ge, putting these values in equations (1) and (2), and divide equations (1) by (2) 
   we get,  $\bold{\frac{2g_e}{g_e}=\frac{GM_p.R_e^2}{GM_e.(\frac{R_e}{2})^2}}\\\\\bold{\frac{M_p}{M_e}=\frac{1}{2}}$

hence, answer is 1 : 2

    

Answer 2

The above answer is correct and could be referred to.

Hope this helps you guys :D