Answer
(a) No; your side of the pulley
(b) your side: 28N; other side: 18N
Work Step by Step
(a) No, the tension in the rope on both sides is not the same. Since the pulley itself has some mass, the tension on your side must be enough to accelerate the pulley as well as the hanging mass. Hence, the tension in the rope on your side is greater.
(b) We can find the required tension as follows:
$T_1=28N$
This is the tension in the rope on your side.
We know that
$T_2=\frac{M(2T_1+mg)}{2M+m}$
We plug in the known values to obtain:
$T_2=\frac{0.67[2(28)+(1.2)(9.81)]}{2(0.67)+1.2}$
$T_2=18N$
