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Problem $2$: Two collars, $\backslash ($ B $\backslash )$ and $\backslash ($ C $\backslash )$ are sliding along rough $(\backslash (\backslash$mu$\_\{\backslash$boldsymbol$\{$k$\}\}\backslash )$ is given$)$ shafts $\backslash ($ A D $\backslash )$ and $\backslash ($ A G $\backslash )$ respectively. Based on the information provided in Figure $2,$ determine the following:

$1.$ Acceleration of $\backslash ($ B $\backslash )$ with respect to $\backslash ($ C $\backslash )($that is $\backslash (\backslash$boldsymbol$\{$a$\}\_\{$B $/$ C$\}\backslash ))(10$ points$)$

$2.$ Normal forces at $\backslash ($ B $\backslash )(10$ points$)$

$3.$ Normal forces at $\backslash ($ C $\backslash )(10$ points$)$

Figure $2$: Problem $2$