Search any question & find its solution
Question:
Answered & Verified by Expert
A force of $-F \hat{\mathbf{k}}$ acts on $O$, the origin of the coordinate system. The torque about the point $(1,-1)$ is
Options:
Solution:
1511 Upvotes
Verified Answer
The correct answer is:
$-F(\hat{\mathbf{i}}+\hat{\mathbf{j}})$
Position vector \(\vec{r}=\mathrm{PO}=\overrightarrow{\mathrm{O}}-(1 \hat{i}-1 \hat{\mathrm{j}})=-\hat{i}+\hat{j}\)
Torque about point \(P, \vec{\tau}=\vec{r} \times \vec{F}\)
\(\begin{aligned}
& \therefore \vec{\tau}=(-\hat{i}+\hat{j}) \times(-F \hat{k}) \\
& \text{OR } \vec{\tau}=F[(\hat{i} \times \hat{k})-(\hat{j} \times \hat{k})]=F[-\hat{j}-\hat{i}] \\
& \Rightarrow \vec{\tau}=-F[\hat{i}+\hat{j}]
\end{aligned}\)
Torque about point \(P, \vec{\tau}=\vec{r} \times \vec{F}\)
\(\begin{aligned}
& \therefore \vec{\tau}=(-\hat{i}+\hat{j}) \times(-F \hat{k}) \\
& \text{OR } \vec{\tau}=F[(\hat{i} \times \hat{k})-(\hat{j} \times \hat{k})]=F[-\hat{j}-\hat{i}] \\
& \Rightarrow \vec{\tau}=-F[\hat{i}+\hat{j}]
\end{aligned}\)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.