Two forces whose magnitudes are in the ratio $3 : 5$ give a resultant of $28 N$ . If the angle of their inclination is $60^{o}$ , find the magnitude of each force.

Open in App

Solution

Let $A$ and $B$ be the two forces.
Then $A = 3 x, B = 5 x; R = 28 N$ and $θ = 60^{o}$ .
Dividing $A$ by $B$ , $\frac{A}{B} = \frac{3}{5}$
We know that $R = \sqrt{a^{2} + B^{2} + 2 A B cos θ}$
$\Rightarrow 28 = \sqrt{(3 x)^{2} + (5 x)^{2} + 2 (3 x) (5 x) cos 60^{o}}$
$= \sqrt{9 x^{2} + 25 x^{2} + 15 x^{2}} = 7 x$
$\Rightarrow x = \frac{28}{7} = 4$
Hence, forces are $A = 3 \times 4 = 12 N, B = 5 \times 4 = 20 N$

Suggest Corrections

Similar questions

3 : 5

28 N

60^{\circ}

60^{\circ}

n

n

3 : 5

35 N

60^{o}

Two forces, whose magnitude are at the ratio of 3:5 give a resultant of 35 N. If angle of inclination is 60^o, then the magnitude of each force is:

Join BYJU'S Learning Program