中四物理科問題 moment

(a) Your equation is wrong, The moment given by the two ropes is
= [2T.sin(45)] x 2 (you probably have neglected that there are two ropes)
Hence, 40g x (2/2) = [2T.sin(45)] x 2
solve for T, the tension in the rope, gives T = 141.4 N

(b) Moment given by the weight of the plank
= 40g x (1.cos(45)) N
Moment given by the 2 ropes
= 2T' x [2.cos(22.5)] where T' is the new rope tension

Hence, 40g x (1.cos(45)) = 2T' x [2.cos(22.5)]
solve for T' gives T' = 76.5 N

No offence:

The answers are right, unit for moment of the weight is not right.

In part (b),
Moment = force x distance
Moment = mass of plank x g x distance (where g is acceleration due to gravity)
Moment = (40 kg) x (10 m s^-2) x (1m cos 45º)
Moment = (400 N) x (0.7071 m )
Moment = 282.84 N.m