If $\vec{F} = (4\hat{i} - 10\hat{j})$ and $\vec{r} = (5\hat{i} - 3\hat{j})$,then calculate the torque $\vec{\tau} = \vec{r} \times \vec{F}$. (in $\hat{k}$)

Find the torque about the origin when a force of $3 \hat{j} \text{ N}$ acts on a particle whose position vector is $2 \hat{k} \text{ m}$.

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 ........ $N-m.$

$A$ door is hinged at one end and is free to rotate about a vertical axis (figure). Does its weight cause any torque about this axis? Give a reason for your answer.

$A$ couple produces

$A$ wheel of radius $20\, cm$ has forces applied to it as shown in the figure. The net torque produced by the forces $4\, N$ at $A$,$8\, N$ at $B$,$6\, N$ at $C$,and $9\, N$ at $D$ at the angles indicated is: