Question

$\text{Statement I:}$
If three forces $\overrightarrow{F_1},\overrightarrow{F_2}$ and $\overrightarrow{F_3}$ are represented by three sides of a triangle and $\overrightarrow{F_1}+\overrightarrow{F_2}=-\overrightarrow{F_3}$, then these forces are concurrent forces and satisfy the condition for equilibrim.

$\text{Statement II :}$
A triangle made up of three forces $\overrightarrow{F_1},\overrightarrow{F_2}$ and $\overrightarrow{F_3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.

In the light of the above statements, choose the most appropriate answer from options given below.

• A. Both $\text{Statement I}$ and $\text{Statement II}$ are true.
• B. Both $\text{Statement I}$ and $\text{Statement II}$ are false
• C. $\text{Statement I}$ is true but $\text{Statement II}$ is false.
• D. $\text{Statement I}$ is false but $\text{Statement II}$ is true

Answer 1

The correct option is A Both $\text{Statement I}$ and $\text{Statement II}$ are true.

Let three forces $\overrightarrow{F_1},\overrightarrow{F_2}$ and $\overrightarrow{F_3}$ are represented by three sides of a triangle

$\text{Statement I}$

Given that $\overrightarrow{F_1}+\overrightarrow{F_2}=-\overrightarrow{F_3}$

$\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}=0$

ie Net force is zero, hence these concurrent forces, satisfy condition of equilibrium.

$\text{Statement II}$

Forces are taken in same order as shown below.


Using triangle law of vectors we get
$\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}=0$
Hence these forces satisfy condition of translatory equilibrium.

Hence, both $\text{Statement I}$ and $\text{Statement II}$ are true.

Therefore, option $\left(A\right)$ is correct.