Question

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 ${}^{\prime }{O}^{\prime }$ and ${}^{\prime }{Q}^{\prime }$ are :

• A. $-15-20\sqrt{3},15-20\sqrt{3}$
• B. $15+20\sqrt{3},15-20\sqrt{3}$
• C. $15-20\sqrt{3},15+20\sqrt{3}$
• D. $-15+20\sqrt{3},15+20\sqrt{3}$

Answer 1

Answer: (A)

$\overrightarrow{F}=4\hat{i}-3\hat{j}$
${\overrightarrow{r}}_1=5\hat{i}+5\sqrt{3}\hat{j}\&{\overrightarrow{r}}_2=-5\hat{i}+5\sqrt{3}\hat{j}$
Torque about ${}^{\prime }{O}^{\prime }$
${\overrightarrow{\tau }}_O={\overrightarrow{r}}_1\times \overrightarrow{F}=(-15-20\sqrt{3})\hat{k}=(15+2D\sqrt{3})(-\hat{k})$
Torque about ${}^{\prime }{Q}^{\prime }$
${\vec{\tau }}_Q={\vec{r}}_2\times \vec{F}=(-15+20\sqrt{3})\hat{k}=(15-20\sqrt{3})(-\hat{k})$