The position vectors of two points are $2\hat i + \hat j + \hat k$ and $2\hat i - 3\hat j + \hat k$,and the linear momentum is $2\hat i + 3\hat j - \hat k$. The angular momentum is:

$A$ mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency $\omega$. The mass $M$ moves with steady speed in a circular path of constant radius $r$. The angular momentum of $M$ about point $A$ is $L_A$,which lies in the positive $z$-direction,and the angular momentum of $M$ about point $B$ is $L_B$. Which of the following statements is correct for this system?

The time dependence of the position of a particle of mass $m = 2 \ kg$ is given by $\vec r(t) = 2t \hat i - 3t^2 \hat j$. Its angular momentum with respect to the origin at time $t = 2 \ s$ is:

$A$ particle of mass $100\,g$ is projected at time $t = 0$ with a speed $20\,ms^{-1}$ at an angle $45^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t = 2\,s$ is found to be $\sqrt{K}\,kg\,m^2/s$. The value of $K$ is $............$ (Take $g = 10\,ms^{-2}$)

$A$ ball of mass $m$ moving with velocity $v$ collides with a wall elastically as shown in the figure. After the impact,the change in angular momentum about point $P$ is:

$A$ particle of mass $m = 5$ is moving with a uniform speed $v = 3\sqrt{2}$ in the $XOY$ plane along the line $Y = X + 4$. The magnitude of the angular momentum of the particle about the origin is .......