$A$ force of $(2\hat i - 4\hat j + 2\hat k) \ N$ acts at a point $(3\hat i + 2\hat j - 4\hat k) \ m$ from the origin. The magnitude of torque is ......... $N-m$.

If $\vec{F} = (5 \hat{i} - 10 \hat{j}) \text{ N}$ and $\vec{r} = (4 \hat{i} - 3 \hat{j}) \text{ m}$,then the torque $\vec{\tau}$ acting on the object will be:

$A$ force of $-F \hat{k}$ acts on $O$,the origin of the coordinate system. The torque about the point $(1, -1)$ is

Four forces are applied to a wheel of radius $10\,cm$ as shown in the figure. The net torque produced by all these forces about $C$ is

$A$ rod of length $l$ is acted upon by a couple as shown in the figure. The moment of the couple is $\tau \text{ Nm}$. If the force at each end of the rod is $F$,then the magnitude of each force is (given $\sin 30^{\circ} = \cos 60^{\circ} = 0.5$):

$A$ body of mass $10 \, kg$ is hanging at rest with the help of a rope wrapped around a cylinder of diameter $0.2 \, m$. The torque applied about the horizontal axis of the cylinder is ....... $N-m$.