Question

Two forces $A$ and $B$ whose magnitude are in the ratio $3:5$ give a resultant of $28 \, \text{N}$ . If the angle of their inclination is $60^{^\circ },$ then the magnitude of force $B$ will be ----- $N$ .

Answer 1

Let $A$ and $B$ be the two forces.
Then $A=3x; \, B=5x, \, R=28N$ and $\theta =60^{^\circ }$ .
We know that $R=\sqrt{A^{2} + B^{2} + 2 A B c o s \theta }$
$\Rightarrow 28=\sqrt{\left(3 x\right)^{2} + \left(5 x\right)^{2} + 2 \left(3 x\right) \left(5 x\right) c o s \left(60\right)^{^\circ }}$
$=\sqrt{9 x^{2} + 25 x^{2} + 15 x^{2}}=7x$
$\Rightarrow x=\frac{28}{7}=4$
Hence, force $B=5\times 4=20 \, \text{N}$