Question

A slob is subjected to two forces ${\vec{F}}_1$ and ${\vec{F}}_2$ of same magnitude F as shown in the figure. Force ${\vec{F}}_2$ is in XY-plane while force $F_1$ acts along z-axis at the point $(2\vec{i}+3\vec{j})$ . The moment of these forces about point O will be :

• A. $(3\hat{i}-2\hat{j}-3\hat{k})F$
• B. $(3\hat{i}+2\hat{j}+3\hat{k})F$
• C. $(3\hat{i}+2\hat{j}-3\hat{k})F$
• D. $(3\hat{i}-2\hat{j}+3\hat{k})F$

Answer 1

Answer: (D)

Torque for $F_1$ force
${\vec{F}}_1=\frac{F}{2}\left(-\hat{i}\right)+\frac{F\sqrt{3}}{2}\left(-\hat{j}\right)$
$\overrightarrow{r_1}=0\hat{i}+6\hat{j}$
$\widehat{{\tau }_{F_1}}=\overrightarrow{r_1}\times {\vec{F}}_1=3F\hat{k}$
Torque for $F_2$ force
$\overrightarrow{F_2}=F\hat{k}$
$\overrightarrow{r_2}=2\hat{i}+3\hat{j}$
$\overrightarrow{{\tau }_{F_2}}=\overrightarrow{r_2}\times \overrightarrow{F_2}=3F\hat{i}+2F\left(-\hat{j}\right)$
${\vec{\tau }}_{net}={\vec{\tau }}_{F_1}+{\vec{\tau }}_{F_2}$
$=3F\hat{i}+2F\left(-\hat{j}\right)+3F\left(\hat{k}\right)$