Question

Three concurrent coplanar forces 1N, 2N and 3N acting along different directions on a body.
A. Can keep the body in equilibrium if 2N and 3N act at right angles.
B. Can keep the body in equilibrium if 1N and 2N act at right angles.
C. Cannot keep the body in equilibrium.
D. Can keep the body in equilibrium if 1N and 3N act at an acute angle.

Answer 1

Hint: In statics, to keep the body in equilibrium the sum of all the forces acting on a body is zero
$\sum \overrightarrow{F}=0$
Here,
$\overrightarrow{{{F}_{1}}},\overrightarrow{{{F}_{2}}},and{{\overrightarrow{F}}_{3}}$ act on a body.

Complete step by step answer:
Let

& \overrightarrow{{{F}_{1}}}=1N \\\ & \overrightarrow{{{F}_{2}}}=2N \\\ & \overrightarrow{{{F}_{3}}}=3N \\\ \end{aligned}$$  We have to find that in which condition we can keep the body in equilibrium. Body in equilibrium when sum of all the forces acting on a body is zero $$\sum \overrightarrow{F}=0$$ $$\overrightarrow{{{F}_{1}}}+{{\overrightarrow{F}}_{2}}+{{\overrightarrow{F}}_{3}}=0$$ It is only possible when $$\left| \overrightarrow{{{F}_{1}}}+{{\overrightarrow{F}}_{2}} \right|=\left| {{\overrightarrow{F}}_{3}} \right|$$ Here, $$\begin{aligned} & \overrightarrow{{{F}_{1}}}=1N \\\ & \overrightarrow{{{F}_{2}}}=2N \\\ & \overrightarrow{{{F}_{3}}}=3N \\\ \end{aligned}$$  Hence, $$\overrightarrow{{{F}_{1}}}and{{\overrightarrow{F}}_{2}}$$should act in one direction and $${{\overrightarrow{F}}_{3}}$$should act in opposite direction of $$\overrightarrow{{{F}_{1}}}and{{\overrightarrow{F}}_{2}}$$ But problem statement says that three concurrent coplanar forces $$\overrightarrow{{{F}_{1}}},\overrightarrow{{{F}_{2}}},and{{\overrightarrow{F}}_{3}}$$acting along different directions on a body. But when$$\overrightarrow{{{F}_{1}}}and{{\overrightarrow{F}}_{2}}$$ act along the same direction then only the body will be in equilibrium. If $$\overrightarrow{{{F}_{1}}}and{{\overrightarrow{F}}_{2}}$$ act along different directions then we cannot keep the body in equilibrium. Hence, option C is correct. Note: If body is not in equilibrium and moving with acceleration a then $$\begin{aligned} & \sum \overrightarrow{F}\ne 0 \\\ & \sum \overrightarrow{F}=\overrightarrow{{{F}_{net}}}={{m}_{net}}\overrightarrow{{{a}_{net}}} \\\ \end{aligned}$$ Acceleration of a moving body can be found by the above formula. Students should remember that if the body is moving with uniform velocity then acceleration will be zero and $$\sum \overrightarrow{F}=0$$.