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

Option 1)

-F\left ( \hat{i}-\hat{j} \right )

Option 2)

F\left ( \hat{i}-\hat{j} \right )

Option 3)

-F\left ( \hat{i}+\hat{j} \right )

Option 4)

F\left ( \hat{i}+\hat{j} \right )

Answers (1)

As we learnt in

Torque -

\underset{\tau }{\rightarrow}= \underset{r}{\rightarrow}\times \underset{F}{\rightarrow}   

 

- wherein

This can be calculated by using either  \tau=r_{1}F\; or\; \tau=r\cdot F_{1}

r_{1} = perpendicular distance from origin to the line of force.

F_{1} = component of force perpendicular to line joining force.

 

 

 

 

given\; \; \; \vec{\tau }=\vec{r}\times \vec{F}

\vec{F}=-F\hat{k},\vec{r}=\hat{i}-\hat{j}

=\hat{i}F-\hat{j}(-F)=F(\hat{i}+\hat{j})


Option 1)

-F\left ( \hat{i}-\hat{j} \right )

This is an incorrect option.

Option 2)

F\left ( \hat{i}-\hat{j} \right )

This is an incorrect option.

Option 3)

-F\left ( \hat{i}+\hat{j} \right )

This is an incorrect option.

Option 4)

F\left ( \hat{i}+\hat{j} \right )

This is the correct option.

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