$A$ force of $3\hat{i} + 2\hat{j} - \hat{k} \text{ N}$ acts on a particle with position vector $\hat{i} + \hat{j} - \hat{k} \text{ m}$. The magnitude of torque of the given force is

The moment of inertia of a disc of radius $0.5\,m$ about its geometric axis is $2\,kg-m^2.$ If a string is tied to its circumference and a force of $10\,N$ is applied,the value of torque with respect to this axis will be ........ $N-m.$

The vector sum of a system of non-collinear forces acting on a rigid body is given to be nonzero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero,does this mean that it is necessarily zero about any arbitrary point?

If force $\vec{F} = 3 \hat{i} + 4 \hat{j} - 2 \hat{k}$ acts on a particle having position vector $\vec{r} = 2 \hat{i} + \hat{j} + 2 \hat{k}$,then the torque about the origin will be:

$A$ wheel of radius $R$ with an axle of radius $R/2$ is as shown in the figure. It is free to rotate about a frictionless axis through its centre and perpendicular to the page. Three forces are exerted as shown in the figure: a force $F$ at an angle of $45^{\circ}$ to the tangent of the outer rim,a force $F$ tangential to the inner axle,and a force $2F$ tangential to the outer rim. The magnitude of the net torque acting on the system is nearly ............. $FR$.

$A$ force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau$ about the origin. Choose the correct option.