question_answer

Three forces P, Q and R acting at a point 0 in the plane. The measure of \[\angle POQ\] and \[\angle QOR\] are \[{{120}^{o}}\] and \[{{90}^{o}}\] respectively. Then, the equilibrium forces P, Q and R are in the ratio

A) \[3:1:2\]        

B) \[2:1:3\]  

C) \[\sqrt{3}:1:2\]

D) \[2:1:\sqrt{3}\]

Correct Answer: D

Solution :

Since, the forces are in equilibrium position, they by Lami?s theorem, \[\Rightarrow \] \[\frac{P}{sin{{90}^{o}}}=\frac{Q}{\sin {{150}^{o}}}=\frac{R}{\sin \,{{120}^{o}}}\] \[\Rightarrow \] \[\frac{P}{1}=\frac{Q}{1/2}=\frac{R}{\sqrt{3}/2}\] \[\Rightarrow \] \[P:Q:R=2:1:\sqrt{3}\]