Question

$P, Q$ and $R$ are three coplanar forces acting at a point and are in equilibium. Given $P=1.9318\, kg\, wt$ $\left[\sin \theta_{1}=0.9659\right]$, the value of $R$ (in $kg$ wt) is

• A. 0.9659
• B. 2
• C. 1
• D. 1/2

Answer 1

Answer: (C)

Using Lami's theorem, we have
$\frac{P}{\sin \theta_{1}}=\frac{R}{\sin 150^{\circ}}$
$\Rightarrow \frac{P}{\sin \theta_{1}}=\frac{R}{\sin \left(180^{\circ}-30^{\circ}\right)}$
$\Rightarrow \frac{1.9318\, kg wt}{0.9659}=\frac{R}{1/2}$
$\Rightarrow R=\frac{1.9318}{0.9659}\times\frac{1}{2}\,kg\,wt = 1\, kg\,wt.$