Question

On the surface of planet y, which has a mass of 4.83x1024 kg, a 30.0 kg object weighs 50.0 n. what is the radius of the planet?

Answer 1

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
$W=mg$
where m=30 kg is the mass of the object. From this, we find g:
$g= \frac{W}{m}= \frac{50.0 N}{30 kg}=1.67 m/s^2$

2) The gravitational acceleration of a planet with mass M and radius r is given by
$g= \frac{GM}{r^2}$
where $G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational  constant. In our problem, the mass of the planet is 
$M=4.83 \cdot 10^{24} kg$, and we found g in step 1), $g=1.67 m/s^2$, so we have everything to solve and find the value of the radius r:
$r= \sqrt{ \frac{GM}{g} }= \sqrt{ \frac{(6.67\cdot 10^{-11})(4.83 \cdot 10^{24})}{1.67} }=1.39\cdot 10^7 m$