Three equal weights of mass 2 kg each are hanging on a string passing over a fixed pulley as shown in the figure. The tension in the string connecting the weights B and C is :

The correct option is B 13N
Since all three blocks masses is equal.

$a=\frac{\text{Resultent force}}{\text{Total mass}}=\frac{2mg-mg}{3m}=\frac{mg}{3m}$

$a=\frac{g}{3}$

Tension between B and C will be

$mg=ma=T_{2}mg-m\times \left(\frac{g}{3}\right)=T_{2}mg-\frac{mg}{3}=T_2{T}_2=\frac{2mg}{3}{T}_2=\frac{2\times 2\times 10}{3}=\frac{40}{3}=13.333$

Hence, correct answer is option A.