Question

The resultant of two forces acting at an angle of ${150}^{\circ }$ is $10$ N and its perpendicular to one of the forces.The two other force is:

• A. $\frac{20}{\sqrt{3}}N$
• B. $\frac{10}{\sqrt{3}}N$
• C. $20N$
• D. $\frac{20}{3}N$

Answer 1

The correct option is C $20N$

Let forces are $A$ and $B$.

$R$ is the resultant force of $A$ and $B$. As shown in figure, $R$ is perpendicular to the $B$.

From the figure, $Acos\left({60}^o\right)=R=10$ $\Rightarrow A=20N$,

$\Rightarrow$ $Asin\left({60}^o\right)=B$ $\Rightarrow B=10\sqrt{3}N$,

$\therefore$ Forces are $20N$ and $10\sqrt{3}$.