Question

In the figure shown below, find the torque due to the force of $5\text{N}$, about point $\text{O}$ and $\text{A}$.

• A. $6\text{Nm}$ along $+z$ direction, $6\text{Nm}$ along $+z$ direction.
• B. $6\text{Nm}$ along $+z$ direction, $6\text{Nm}$ along $-z$ direction
• C. $6\text{Nm}$ along $-z$ direction, $6\text{Nm}$ along $-z$ direction
• D. $6\text{Nm}$ along $-z$ direction, $6\text{Nm}$ along $+z$ direction

Answer 1

The correct option is D $6\text{Nm}$ along $-z$ direction, $6\text{Nm}$ along $+z$ direction

Given, $|\overrightarrow{F}|=5\text{N}$
$\Rightarrow \overrightarrow{F}=4\hat{i}+3\hat{j}$
(from the diagram)

To find torque about ${}^{\prime }{\text{O}}^{\prime }$:
$\overrightarrow{\tau }=\overrightarrow{OB}\times \overrightarrow{F}$
Here, $\overrightarrow{OB}=2\hat{i}+3\hat{j}$
$\overrightarrow{\tau }=\left|\begin{array}{ccc}i& j& k\\ 2& 3& 0\\ 4& 3& 0\end{array}\right|=-6\hat{k}\text{Nm}$


To find torque about ${}^{\prime }{\text{A}}^{\prime }$:
$\overrightarrow{r}=\overrightarrow{AB}=2\hat{i}$
Torque $\left(\overrightarrow{\tau }\right)=\overrightarrow{AB}\times \overrightarrow{F}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 0& 0\\ 4& 3& 0\end{array}\right|$
$=6\hat{k}\text{Nm}$