Q107 / 160 · JIPMER 2009 · Physics

A force of $-F \hat{\mathbf{k}}$ acts on $O$, the origin of the coordinate system. The torque about the point $(1,-1)$ is Figure

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

Solution

Position vector \(\vec{r}=\mathrm{PO}=\overrightarrow{\mathrm{O}}-(1 \hat{i}-1 \hat{\mathrm{j}})=-\hat{i}+\hat{j}\) Torque about point \(P, \vec{\tau}=\vec{r} \times \vec{F}\) \(\begin{aligned} & \therefore \vec{\tau}=(-\hat{i}+\hat{j}) \times(-F \hat{k}) \\ & \text{OR } \vec{\tau}=F[(\hat{i} \times \hat{k})-(\hat{j} \times \hat{k})]=F[-\hat{j}-\hat{i}] \\ & \Rightarrow \vec{\tau}=-F[\hat{i}+\hat{j}] \end{aligned}\)

Hence, the correct answer is option: 'B'.

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