$3)$

A $6-kg$ block $B$ rests as shown on a $10-kg$ bracket $A.$ The coefficients of friction are ${}_s=0\mathrm{.}30$ and ${}_k=0\mathrm{.}25$ between block $B$ and bracket $A,$ and there is no friction in the pulley or between the bracket and the horizontal surface. $($a$)$ Determine the maximum mass of block $C$ if block $B$ is not to slide on bracket $A.($b$)$ If the mass of block $C$ is $10\%$ larger than the answer found in $a,$ determine the accelerations of $A,B$ and $C.$