A slab is subjective to two forces of same magnitude F as shown in the figure. Force is in XY-plane while force F1 acts along z-axis at the point . The moment of these forces about point O will be:

Engineering

Physics

Torque and Equilibrium of Rigid Bodies

Question

A slab is subjective 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 F₁ acts along z-axis at the point $(2 \vec{i} + 3 \vec{j})$ . The moment of these forces about point O will be:

$(3 \vec{i} - 2 \vec{j} + 3 \hat{k}) F$

$(3 \vec{i} + 2 \vec{j} + 3 \hat{k}) F$

$(3 \vec{i} - 2 \vec{j} - 3 \hat{k}) F$

$(3 \vec{i} + 2 \vec{j} - 3 \hat{k}) F$

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${\vec{τ}}_{0} = {\vec{τ}}_{1} + {\vec{τ}}_{2}$

$= (6 \hat{i}) \times (- \frac{F}{2} \hat{i} + \frac{F \sqrt{3}}{2} \hat{j}) + (2 \hat{i} + 3 \hat{j}) \times (F \hat{k})$

$= - 3 F \hat{k} (- 2 F \hat{j} + 3 F \hat{i})$

$= F (3 \hat{i} - 2 \hat{j} - 3 \hat{k})$