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 :
 
Option: 1 -15-20\sqrt{3},15-20\sqrt{3}
Option: 2 15-20\sqrt{3},15+20\sqrt{3}
Option: 3 15+20\sqrt{3},15-20\sqrt{3}  
Option: 4 -15+20\sqrt{3},15+20\sqrt{3}

Answers (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}})
Torque about 'Q'
\vec{\tau}_{Q}=\overrightarrow{\mathrm{r}}_{2} \times \overrightarrow{\mathrm{F}}=(-15+20 \sqrt{3}) \hat{\mathrm{k}}=(15-20 \sqrt{3})(-\hat{\mathrm{k}})

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