Question

Three forces of magnitude $30,60$ and $\mathrm{P}$ acting at a point are in equilibrium. If the angle between the first two is $60°$, the value of $\mathrm{P}$ is

• A. $30\sqrt{7}$
• B. $30\sqrt{3}$
• C. $20\sqrt{6}$
• D. $25\sqrt{2}$

Answer 1

The correct option is A

$30\sqrt{7}$

The explanation for the correct answer.

Find the magnitude of $\mathrm{P}$

Given: Magnitude of two forces $30,60$ and the angle between them is $60°$

The magnitude of $\mathrm{P}$ is equal to the resultant of the other two forces.

Resultant $=\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2+2\mathrm{abcos\theta }}$

$$\begin{gathered} \mathrm{P}=\sqrt{{30}^2+{60}^2+2\times 30\times 60\times \cos 60°} \\ \mathrm{P}=\sqrt{900+3600+3600\times \frac{1}{2}} \\ \mathrm{P}=\sqrt{6300} \\ \mathrm{P}=30\sqrt{7} \end{gathered}$$

Hence option (a) is the correct answer.