The position vector of a $1\,kg$ object is $\overrightarrow{r} = (3\hat{i} - \hat{j})\,m$ and its velocity is $\overrightarrow{v} = (3\hat{j} + \hat{k})\,m/s$. The magnitude of its angular momentum is $\sqrt{x}\,N\cdot m\cdot s$,where $x$ is:

$A$ uniform rod of mass $m$ and length $l$ is moving with velocity $u$ in a direction perpendicular to its length. $A$ blow of impulse $J$ is applied in the direction of $u$,perpendicular to its length at a distance $l/4$ from its center at point $P$,such that the instantaneous velocity of point $P$ is $2u$. Then the velocity of its center of mass will be:

Two rotating bodies have the same angular momentum,but their moments of inertia are $I_1$ and $I_2$ respectively. If $I_1 > I_2$,which body will have a higher kinetic energy?

$A$ disc of mass $M$ and radius $R$ is rolling on a horizontal surface as shown in the figure. What is the magnitude of the angular momentum of the disc about the origin $O$?

$A$ particle of mass $m$ moves with a constant velocity. Which of the following statements is incorrect regarding its angular momentum?

Explain the Cartesian components of the angular momentum of a particle.