Question

Two coplanar concurrent forces $P_1=2t$ and $P_2=2t$ meeting at $O$ act on a lamina at 45° as shown in figure.


From the force diagram the force R to be applied at $O$ in order to keep the body in equilibrium is given by

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The force $R$ should be opposite to the resultant of ${\overrightarrow{P}}_1$ and ${\overrightarrow{P}}_2$
Resultatn of ${\overrightarrow{P}}_1$ and ${\overrightarrow{P}}_2={\overrightarrow{P}}_1+\overrightarrow{P_2}$
$\therefore R=-{\overrightarrow{P}}_1-{\overrightarrow{P}}_2$
In other words, $\overrightarrow{R}+{\overrightarrow{P}}_1+{\overrightarrow{P}}_2=0$. i.e. $\overrightarrow{R},{\overrightarrow{P}}_1$ and ${\overrightarrow{P}}_2$ should form a closed triangle.