$A$ particle of mass $2 \ kg$ located at the position $(\hat{i} + \hat{j}) \ m$ has a velocity $2(\hat{i} - \hat{j} + \hat{k}) \ m/s$. Its angular momentum about the $z$-axis in $kg \cdot m^2/s$ is:

$A$ point mass $m$ is attached to one end of a string passing through a cylindrical tube. The string is held in hand,and the point mass moves in a horizontal circle of radius $r_1 = 2 \ m$ with a speed of $v_1 = 4 \ m/s$. The string is then pulled down so that the radius is reduced to $r_2 = 1 \ m$. Calculate the new linear velocity,angular velocity,and the ratio of the final kinetic energy to the initial kinetic energy.

$A$ ball of mass $1 \,kg$ is projected with a velocity of $20 \sqrt{2} \,m/s$ from the origin of an $xy$ coordinate axis system at an angle of $45^{\circ}$ with the $x$-axis (horizontal). The angular momentum [in $SI$ units] of the ball about the point of projection after $2 \,s$ of projection is [take $g = 10 \,m/s^2$] ($y$-axis is taken as vertical).

$A$ particle moves along a circular path with decreasing speed. Hence,

$A$ 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 moves in a circular path with decreasing speed. Choose the correct statement.