In the figure shown, find the tension in the string connecting the blocks of mass $2kg$ and $3kg$. Take $g=10m/s^2$

The correct option is C $13.6N$
Considering $2kg$ and $3kg$ masses as a system, we have from the FBDs as


$f_1={\mu }_1\left(2g\right)=0.3\times 20=6N$
and, $f_2={\mu }_2\left(3g\right)=0.2\times 30=6N$
Also, equation of force can be written as
$5g-T_1=5a$..........(i)
$T_1-(f_1+f_2)=5a$......(ii)
Thus, from eq (i) and (ii) we get
$5g-(f_1+f_2)=10a$
$a=\frac{50-(6+6)}{10}=\frac{38}{10}=3.8m/s^2$

Now, from the FBD of $2kg$ mass we get


$T-f_1=2a$
$T=f_1+2a=6+2\left(3.8\right)$
$\Rightarrow T=13.6N$