One possible design for spacecraft that create artificial gravity $($used in the movie "Stowaway" pictured above$)$ involves two inhabitable modules $($each with a mass of $750$ kg $)$ connected by long cables $($lets say $100\mathrm{.}0$ m each$)$ spinning around a common center. Suppose this craft and its $10$ crew members $($each with mass $50$ kg $)$ are initially spinning at $0\mathrm{.}31$ radians $\frac{?}{sec}$ to create normal earth gravity in the extended modules. If all $10$ crew members climbed to within $3\mathrm{.}0$ m of the center to perform maintenance, what is the new rate of spin?

$0\mathrm{.}13ra\frac{d}{sec}$

$0\mathrm{.}52ra\frac{d}{sec}$

$0\mathrm{.}41ra\frac{d}{sec}$

$0\mathrm{.}73ra\frac{d}{sec}$

$0\mathrm{.}64ra\frac{d}{sec}$