A force of -F k acts on O , the origin of the coordinate system....

A force of

-F \hat{\mathbf{k}}

acts on

O

, the origin of the coordinate system. The torque about the point

(1,-1)

Options

A $F(\hat{\mathbf{i}}-\hat{\mathbf{j}})$
B $-F(\hat{\mathbf{i}}+\hat{\mathbf{j}})$
C $F(\hat{\mathbf{i}}+\hat{\mathbf{j}})$
D $-F(\hat{\mathbf{i}}-\hat{\mathbf{j}})$

Correct answer

B. $-F(\hat{\mathbf{i}}+\hat{\mathbf{j}})$

Step-by-step solution

Position vector (\vec{r}=\mathrm{PO}=\overrightarrow{\mathrm{O}}-(1 \hat{i}-1 \hat{\mathrm{j}})=-\hat{i}+\hat{j}) Torque about point (P, \vec{\tau}=\vec{r} \times \vec{F})

\begin{aligned} & \therefore \vec{\tau}=(-\hat{i}+\hat{j}) \times(-F \hat{k}) \\ & \text{OR } \vec{\tau}=F[(\hat{i} \times \hat{k})-(\hat{j} \times \hat{k})]=F[-\hat{j}-\hat{i}] \\ & \Rightarrow \vec{\tau}=-F[\hat{i}+\hat{j}] \end{aligned}

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