## Physics (10th Edition)

$r_A/r_B=0.775$
The weight of an object with mass $m$ on planet A with mass $M_A$ and radius $r_A$ is $$W_A=G\frac{mM_A}{r_A^2}$$ Similarly, the weight of the same object on planet B is $$W_B=G\frac{mM_B}{r_B^2}$$ As the weight of this object is the same on both planets, we have $$G\frac{mM_A}{r_A^2}=G\frac{mM_B}{r_B^2}$$ $$\frac{M_A}{r^2_A}=\frac{M_B}{r^2_B}$$ $$\frac{r^2_A}{r^2_B}=\frac{M_A}{M_B}=0.6$$ $$\frac{r_A}{r_B}=\sqrt{0.6}=0.775$$