When the position vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ changes sign to $-\vec{r}$, which one of the following vectors will not flip its sign?

$A$ thin horizontal disc is rotating about a vertical axis passing through its fixed centre $O$. Its angular momentum is $L_A$ and $L_B$ computed about points $A$ and $B$, respectively, with $OB = 2 \times OA$. The value of $\frac{L_A}{L_B}$ is :

If the Earth is considered a sphere of radius $R$ and mass $M$,then its angular momentum about its axis of rotation in terms of the time period $T$ will be:

$A$ particle of mass $m$ moves along a straight line $AB$ in the $XY$ plane. Let $L_A$ and $L_B$ be the angular momentum of the particle about the origin $O$ when it is at points $A$ and $B$ respectively. Then:

$A$ particle is moving along a straight line parallel to $x-$ axis with constant velocity. Its angular momentum about the origin

$A$ 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.