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

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 $hat{k}$)

Which of the following is a vector quantity?

$A$ force $\overrightarrow{F} = (\hat{i} + 2\hat{j} + 3\hat{k}) \text{ N}$ acts at a point $\vec{r}_1 = (4\hat{i} + 3\hat{j} - \hat{k}) \text{ m}$. The magnitude of torque about the point $\vec{r}_2 = (\hat{i} + 2\hat{j} + \hat{k}) \text{ m}$ is $\sqrt{x} \text{ N-m}$. The value of $x$ is $........$

$A$ triangular plate is shown in the figure. $A$ force $\overrightarrow{F} = 4 \hat{i} - 3 \hat{j}$ is applied at point $P$. The torques at point $P$ with respect to point $O$ and point $Q$ are:

$A$ uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. $A$ horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face,at a height $\frac{3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to tilt about the edge is (assume that the cube does not slide):