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A couple has moment G, and the magnitude of each force in the couple is P. When the force P is rotated by 90°, the new couple formed has moment H. If the same force P is instead rotated through an angle α, the moment of the couple becomes

1. H sin α − G cos α
2. G sin α − H cos α
3. H sin α + G cos α
4. G sin α + H cos α

Correct answer: H sin α + G cos α

Solution

The moment of a couple is determined by the perpendicular distance between the lines of action of the forces. When one force is rotated through an angle α, the new moment can be expressed as the sum of the original moment G adjusted by the cosine of α and the new moment H adjusted by the sine of α, leading to the correct expression H sin α + G cos α.

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