A force of $-F_k$ acts on $O$, the origin of the coordinate system. The torque about the point $(1, -1)$ is.

1. $-\mathit{\text{F}}\left(\hat{\text{i}}-\hat{\text{j}}\right)$
2. $\mathit{\text{F}}\left(\hat{\text{i}}-\hat{\text{j}}\right)$
3. $-\mathit{\text{F}}\left(\hat{\text{i}}+\hat{\text{j}}\right)$
4. $\mathit{\text{F}}\left(\hat{\text{i}}+\hat{\text{j}}\right)$

Solution

$\overrightarrow{\tau }=\overrightarrow{\text{r}}\times \overrightarrow{\text{F}}$




Find the position vector with respect to O(origin) is $\overrightarrow{\text{r}}$

$\overrightarrow{F}=-\text{F}\widehat{k}$

$\overrightarrow{r}=-\hat{\mathrm{i}}+\hat{\mathrm{j}}$

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$

$=\left(-\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)\times F\left(-\hat{\mathrm{k}}\right)$

$=\left(-\hat{\mathrm{j}}+-\hat{\mathrm{i}}\right)F$

$=F\left(-\hat{\mathrm{i}}-\hat{\mathrm{j}}\right)$

Asked in: MHT CET Full Test 2

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