Let's model a planetary ring as having mass $M_{\text{r}\text{i}\text{n}\text{g}}=2\mathrm{.}09{10}^{20}kg$ and radius $R=100,000km.$ A body of mass $m=1,000kg$ is placed at a point $A$ on the axis of the ring, $2\mathrm{.}00{10}^{8}m$ from the center of the ring $($figure$).$ When the object is released, the attraction of the ring makes the object move along the axis toward the center of the ring $($point B$).$

$4$

$($a$)$ Calculate the gravitational potential energy $($in J$)$ of the object$-$ring system when the object is at $A.$

$q,$ J

$($b$)$ Calculate the gravitational potential energy $($in J$)$ of the system when the object is at B$.$

$$

$($c$)$ Calculate the speed $($in $\frac{m}{s})$ of the object as it passes through $B.$

$q,\frac{m}{s}$