Question 36: Centre of Mass and Rotational Motion

Question

A force of $-\mathrm{F} \hat{\mathbf{i}}$ acts at the origin of the coordinate system. The torque about the point $(0,1,-1)$ is:

Accepted Answer

Let the moment point be $P=(0,1,-1)$ and the force applied at the origin $O=(0,0,0)$.  Then
Position vector from $P$ to $O$ is
$     \mathbf{r} = \overrightarrow{PO} = (0,0,0)-(0,1,-1) = (0,-1,1).   $
Force vector is
$     \mathbf{F} = -F\,\hat{\mathbf{i}} = (-F,0,0).   $
The torque about $P$ is
$     \boldsymbol{	au} = \mathbf{r}	imes\mathbf{F}       = \bigl(0,-1,1\bigr)	imes\bigl(-F,0,0\bigr)       = -F\,\hat{\jmath}\;-\;F\,\hat{\mathrm{k}}       = -F\bigl(\hat{\jmath}+\hat{\mathrm{k}}\bigr).   $
Hence the correct choice is Option B.

Answer

$F(\hat{\jmath}+\hat{\mathrm{k}})$

Answer

$-F(\hat{\jmath}+\mathrm{k})$

Answer

$F(\hat{\mathrm{i}}+\mathrm{k})$

Answer

$-F(\hat{\imath}+\hat{\jmath})$

Centre of Mass and Rotational Motion

A force of -\mathrm{F} \hat{\mathbf{i}} acts at the origin of the coordinate system. The torque about the point (0,1,-1) is:

Choose the correct answer: