In the figure shown, the tension at the midpoint of the rope of mass $3\text{kg}$ (point $B$) is $13\text{N}$. Find the force pulling the $5\text{kg}$ body.

The correct option is A $10\text{N}$
Let the tension at the mid-point $B$ of the rope be $T_B$
So, the acceleration of the system is given by,


From the above FBD we have,
$T_B=(5+1.5)a$
$13=6.5a$ (As given $T_B=13N$)
$\Rightarrow a=2{\text{m/s}}^2$

The pulling force for the $5Kg$ mass will be the tension in the rope at point A
So, let the tension be $T_A$


From the FBD of $5\text{kg}$ body we have,
$T_A=Mass\times acceleration=5\times 2$
$=10\text{N}$
Thus, the pulling force for $5Kg$ mass is $10N$