Question

Two forces whose magnitude are in the ratio $9:11$ give a resultant of $38$ N. If the angle of their inclination is $30^{\circ }$ then what will be the magnitude of each force?

• A. $19.8N,24.2N$
• B. $20N,24N$
• C. $25N,30N$
• D. None of these

Answer 1

Answer: (A)

Let the two forces $A$ and $B$
$A=9x,B=11x\theta =30$
$\therefore \frac{A}{B}=\frac{9}{11}$
$R=\sqrt{A^2+B^2+2AB\cos \theta }$
$38=\sqrt{(9x{)}^2+(11x{)}^2+2\times 9x\times 11x\times \frac{1}{2}}$
$38=\sqrt{81x^2+121x^2+99x^2}$
$38=\sqrt{301x^2}$
$38=17.3x\Rightarrow x=\frac{38}{17.34}=2.19\approx 2.2$
Thus $=A=9\times x=9\times 2.2=19.8N$
$B=11x=11\times 2.2=24.2N$