A) \[G\,\cos \,\theta -H\,\sin \theta \]
B) \[-G\,\cos \,\theta +H\,\sin \theta \]
C) \[G\,\cos \,\theta +H\,\sin \theta \]
D) \[G\,sin\,\theta +H\,\cos \theta \]
Correct Answer: C
Solution :
Moment of couple in certain direction \[G=P.\,\,\,\,\,AM=Pd\,\,\sin \alpha \] [where P is force and d \[\sin \,\alpha \] is arm of couple] Moment of couple, \[H=Pd\,\,\sin \,({{90}^{o}}+\alpha )\] \[=Pd\,\,\cos \,\,\alpha \] when force is turned through an angle \[\theta ,\] then moment of couple \[=Pd\,\,\sin \,(\alpha +\theta )\] \[=Pd(\sin \alpha \,\cos \theta \,+\cos \,\alpha \,\sin \theta )\] \[=\cos \,\theta \,(Pd\,\sin \alpha )+\sin \theta (Pd\,\cos \,\alpha )\] \[=G\,\,\cos \,\,\theta +H\,\,\sin \theta \]You need to login to perform this action.
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