A triangular plate is shown.


A triangular plate is shown. A force $\vec{F}=4 \hat{i}-3 \hat{j}$ is applied at point $P$. The torque at point $P$ with respect to point ' $\mathrm{O}^{\prime}$ and $^{\prime} \mathrm{Q}^{\prime}$ are :

  1. (1) $-15-20 \sqrt{3}, 15-20 \sqrt{3}$

  2. (2) $15+20 \sqrt{3}, 15-20 \sqrt{3}$

  3. (3) $15-20 \sqrt{3}, 15+20 \sqrt{3}$

  4. (4) $-15+20 \sqrt{3}, 15+20 \sqrt{3}$

Correct Option: 1



$\overrightarrow{\mathrm{F}}=4 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}$

$\overrightarrow{\mathrm{r}}_{1}=5 \hat{\mathrm{i}}+5 \sqrt{3} \hat{\mathrm{j}} \& \overrightarrow{\mathrm{r}}_{2}=-5 \hat{\mathrm{i}}+5 \sqrt{3} \hat{\mathrm{j}}$

Torque about 'O'

$\vec{\tau}_{0}=\overrightarrow{\mathrm{r}}_{1} \times \overrightarrow{\mathrm{F}}=(-15-20 \sqrt{3}) \hat{\mathrm{k}}=(15+20 \sqrt{3})(-\hat{\mathrm{k}})$

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