Question

If the resultant of two forces of magnitudes P and Q acting at a point at an angle of 60 degree is $\sqrt{7}Q$ then P/Q is

• A. $1$
• B. $1.5$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

Given that $\left|\overrightarrow{F_1}\right|=P;\left|\overrightarrow{F_2}\right|=Q$

Resultant of two force $=\sqrt{7}Q$

Degree $={60}^o$

Resultant of two force $=\sqrt{{\left|F_1\right|}^2+{\left|F_2\right|}^2+2\left|F_1\right|\left|F_2\right|\cos {60}^o}$

${\left(\sqrt{7}Q\right)}^2=P^2+Q^2+2PQ\cos {60}^o$

$7Q^2=P^2+Q^2+PQ\times \frac{1}{2}$

dividing both side $Q^2$

$7={\left(\frac{P}{Q}\right)}^2+1+\left(\frac{P}{Q}\right)$

${\left(\frac{P}{Q}\right)}^2=-\frac{P}{Q}+6$

${\left(\frac{P}{Q}\right)}^2+\frac{P}{Q}+6=0$

then factor $(\frac{P}{Q}-2)(\frac{P}{Q}+3)=0$

$\frac{P}{Q}=2;\frac{P}{Q}=3$