Question

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

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

Answer 1

Answer: (A)

Resultant of two forces $P$ and $Q$ making an angle $\alpha$ with each other, is
$R=\sqrt{P^2+Q^2+2PQcos\alpha }$
Since, forces of magnitude $30$, $60$ and $P$ are in equilibrium, then magnitude of $P$ is equal to the magnitude of resultant of forces of magnitude $30$ and $60$
$\therefore P=\sqrt{{\left(30\right)}^2+{\left(60\right)}^2+2\left(30\right)\left(60\right)cos60^{\circ }}$
$=\sqrt{900+3600+3600\times \frac{1}{2}}$
$=\sqrt{4500+1800}=\sqrt{6300}$
$=30\sqrt{7}$