Question

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

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

Answer 1

The correct option is D $F(\hat{i}+\hat{j})$

First of all we determine the displacement vector with respect to origin and then cross product of this displacement vector along with the force vector to determine the torque produced by given force about a desired point. The torque about point (1,-1)

$\tau =(\hat{i}-\hat{j})\times (-F\hat{k})$ [as $\tau =r\times F$ and $r=\hat{i}-\hat{j}$]

$⟹\tau =F(-\hat{i}\times \hat{k})+(\hat{j}\times \hat{k})⟹\tau =F[\hat{j}+\hat{i}]$

is the torque about the point (1,−1)