Question

The resultant of two forces acting at an angle of ${120}^o$ is 10 kg -wt and is perpendicular to one of the forces. That force is

• A. $10\sqrt{3}kg-wt$
• B. $20\sqrt{3}kg-wt$
• C. $10kg-wt$
• D. $\frac{10}{\sqrt{3}}kg-wt$

Answer 1

The correct option is C $10kg-wt$

Let $F_1$ & $F_2$ be two forces

$F_R$ is resultant of $F_1$ & $F_2$

Given that $F_R=10kg-wt$

$F_R\perp F_1$,

The component of $F_2$ along $F_R$ is equal to $F_R$

The component $\perp$ar to $F_R$ is equal to $F_1$

$\Rightarrow F_2\cos {30}^o=F_R$

$F_2\sin {30}^o=F_1$

$\Rightarrow F_2\times \frac{\sqrt{3}}{2}=F_R=10kg-wt$

$\Rightarrow F_2=\frac{20}{\sqrt{3}}kg-wt$

Now,

$F_1=F_2\sin 30=\frac{20}{\sqrt{3}}\times \frac{1}{2}=\frac{10}{\sqrt{3}}kg-wt$

Hence

$F_1=\frac{10}{\sqrt{3}}kgwt$.