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

Moment of a force of magnitude $20 \, N$ acting along the positive $x$-direction at point $(3 \, m, 0, 0)$ about the point $(0, 2, 0)$ (in $N \cdot m$) is ...........

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:

$A$ door $1.2 \,m$ wide requires a force of $1 \,N$ to be applied perpendicularly at the free end to open or close it. The perpendicular force required at a point $0.2 \,m$ distant from the hinges for opening or closing the door is: (in $\,N$)

For a particle moving in a circular path under the influence of a central force,the angular momentum remains constant because .......

$A$ couple produces