Answer
(a) less than
(b) $3.22N$
Work Step by Step
(a) We know that the tension in the rope should be less than the weight of the bucket. If these two forces were equal then they would balance each other and as a result there would be no acceleration.
(b) We can calculate the tension in the string as follows:
$a=(\frac{M}{M-\frac{1}{2}m})g$
We plug in the known values to obtain:
$a=(\frac{2.85}{2.85+\frac{1}{2}(0.742)})(9.81)$
$a=8.68m/s^2$
Now $T=\frac{1}{2}ma$
$\implies T=\frac{1}{2}(0.742)(8.68)$
$T=3.22N$
