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Q.
A triangular plate is shown. A force $\overrightarrow{ F }=4 \hat{ i }-3 \hat{ j }$ is applied at point $P$. The torque at point $P$ with respect to point $'O'$ and $'Q'$ are :
JEE MainJEE Main 2021System of Particles and Rotational Motion
Solution:
$\overrightarrow{ F }=4 \hat{ i }-3 \hat{ j }$
$\overrightarrow{ r }_{1}=5 \hat{ i }+5 \sqrt{3} \hat{ j } \,\& \,\,\overrightarrow{r}_{2} =-5 \hat{ i }+5 \sqrt{3} \hat{ j }$
Torque about $'O'$
$\overrightarrow{\tau}_{O}=\overrightarrow{ r }_{1} \times \overrightarrow{ F }=(-15-20 \sqrt{3}) \hat{ k }=(15+2 D \sqrt{3})(-\hat{ k })$
Torque about $'Q'$
$\vec{\tau}_{Q}=\vec{r}_{2} \times \vec{F}=(-15+20 \sqrt{3}) \hat{k}=(15-20 \sqrt{3})(-\hat{k})$
