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

Answer 1

Answer: (A)

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