When you find the moment of a force (or the turning effect/torque. They're all pretty much the same thing), it can be used to find out if a system is in equilibrium or not, like in this question. It also comes up whenever you're looking at rotational motion.
You could call the moment a "turning force" I guess, just instead of pulling or pushing something, you're rotating it instead. When you apply a force to something that's on a pivot, it starts to rotate. The moment's just a measure of the ability of a force to make something rotate.
If the 30N load is supposed to be 10N, I'd just multiply that 10N by the 0.3m distance for the moment. What did you do to get 280Nm? As for 2, for the system to be in equilibrium (balanced) the moment caused by the load on the hand should be equal but opposite to the moment caused by the effort. If both moments weren't the same, the system would start to rotate and it wouldn't be in equilibrium.
It's like dealing with forces, if you push something equally hard with 2 forces in opposite directions, it won't move. If you have equal moments in opposite directions, it won't rotate.
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