A weight W $W$rests on the bar$AB$ as shown in figure. The cable connecting Wand $B$ passes over frictionless pulleys. If bar $AB$ has negligible weight, the vertical component of reaction at $A$ is

$FBD$ of rod will be as shown below 

Summation of moments about $A$ should be zero

$$\begin{gathered} \sum M_A=0=-T_B\times L +(W-T_B)\times a=0 \\ \Rightarrow T_B=\frac{Wa}{\left(L+a\right)} \end{gathered}$$

Summation of moments about $B$ should be zero

$$\begin{gathered} \sum M_B=0=(T_B-W)\times (L-a)+R_{AV}\times L=0 \\ \Rightarrow R_{AV} =W\left(\frac{L-a}{L+A}\right) \end{gathered}$$