Question

If the resultant of two forces of magnitudes P and Q acting at a point at an angle of 60⁰ is (root 7)Q , then P/Q is _________ .

Answer 1

$$\begin{gathered} Resul\tan tofthetwoforcesisgivenby: \\ R=\sqrt{p^2+Q^2+2pQ\cos \theta } \\ R=\sqrt{7}Q \\ \theta ={60}^o \\ \sqrt{7}Q=\sqrt{p^2+Q^2+2pQ\cos 60} \\ squaringbothsides, \\ 7Q^2=p^2+Q^2+2pQ\frac{1}{2} \\ Divideby{Q}^2 \\ 7={\left(\frac{p}{Q}\right)}^2+1+\frac{p}{Q} \\ Let\frac{p}{Q}=x \\ weget \\ {x}^2+x-6=0 \\ onsolvingweget \\ x=2andx=-3 \\ therefore \\ \frac{p}{Q}=2or\frac{p}{Q}=-3 \end{gathered}$$