Question

Three coplanar forces keep a body in equilibrium. The angles between adjacent forces are in the ratio of $3:4:5$. The ratio of maximum force to the minimum force is

• A. $\frac{5}{3}$
• B. $\frac{5}{4}$
• C. $\frac{4}{3}$
• D. $2$

Answer 1

The correct option is D $2$

Ratio of angles=3:4:5

$12\theta =360\therefore \theta =30$

$\therefore$ the angles are${90}^{\circ }{,120}^{\circ },\&{150}^{\circ }$

From the geometry is clear that largest force is $F_s$

$F_{s}sin30=F_2\&F_{3}cos30=F_1\therefore F_2$ is the smallest force

$\because sin30<cos30$

$\frac{F_3}{F_2}=\frac{1}{sin30}=2$