In a balance computation, when an item located aft of the datum is removed, the change in moment is computed as:

In a balance computation, when an item located aft of the datum is removed, the change in moment is computed as:

• A. Weight × Arm
• B. (-)Weight × (+)Arm
• C. (-)Moment × (+)Arm
• D. (+)Weight × (-)Arm

Answer: (B)

Moment about the datum is the product of weight and its arm. In the usual sign convention, the arm forward or aft is given a direction, with aft treated as positive. When you remove an item located aft of the datum, the moment it contributed is no longer there, so the change in total moment is the negative of that contribution. If the item has weight W and is a distance a aft of the datum, its original moment is W×a, and removing it changes the moment by -W×a. This negative sign reflects the loss of that aft-directed moment. That’s why the correct expression is negative weight times the aft arm. The other formulations would either imply adding that moment or misapplying the sign convention for the arm.

Moment about the datum is the product of weight and its arm. In the usual sign convention, the arm forward or aft is given a direction, with aft treated as positive. When you remove an item located aft of the datum, the moment it contributed is no longer there, so the change in total moment is the negative of that contribution. If the item has weight W and is a distance a aft of the datum, its original moment is W×a, and removing it changes the moment by -W×a. This negative sign reflects the loss of that aft-directed moment.

That’s why the correct expression is negative weight times the aft arm. The other formulations would either imply adding that moment or misapplying the sign convention for the arm.