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) $
$ \vec{r_{1}} = 0\hat{i} +6\hat{j} $
$ \hat{\tau_{F_1}} =\vec{r_{1} } \times\vec{F}_{1} = 3F \hat{k} $
Torque for $F_2$ force
$ \vec{F_{2}} = F \hat{k}$
$ \vec{r_{2}} = 2\hat{i} +3\hat{j} $
$ \vec{\tau_{F_2}} = \vec{r_{2}} \times \vec{F_{2}} = 3 F\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) $