We can solve the problem in two steps:
1) From the weight W=50.0 N of the object, we can find the value of the gravitational acceleration g of the planet. In fact, the weight is equal to
[tex]W=mg[/tex]
where m=30 kg is the mass of the object. From this, we find g:
[tex]g= \frac{W}{m}= \frac{50.0 N}{30 kg}=1.67 m/s^2 [/tex]
2) The gravitational acceleration of a planet with mass M and radius r is given by
[tex]g= \frac{GM}{r^2} [/tex]
where [tex]G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}[/tex] is the gravitational constant. In our problem, the mass of the planet is
[tex]M=4.83 \cdot 10^{24} kg[/tex], and we found g in step 1), [tex]g=1.67 m/s^2[/tex], so we have everything to solve and find the value of the radius r:
[tex]r= \sqrt{ \frac{GM}{g} }= \sqrt{ \frac{(6.67\cdot 10^{-11})(4.83 \cdot 10^{24})}{1.67} }=1.39\cdot 10^7 m [/tex]
