Consider a particle of mass $m$ having linear momentum $\vec p$ at position $\vec r$ relative to the origin $O$ . Let $\vec L$ be the angular momentum of the particle with respect the origin. Which of the following equations correctly relate $(s)\, \vec r,\,\vec p$ and $\vec L$ ?

Two particles, each of mass $m$ and speed $v$, travel in opposite directions along parallel lines separated by a distance $d$. Show that the angular momentum vector of the two particle system is the same whatever be the point about which the angular momentum is taken.

A solid sphere rolls without slipping on a rough surface and the centre of mass has a  constant speed $v_0$. If the mass of the sphere is $m$ and its radius is $R$, then find  the angular momentum of the sphere about the point of contact

A particle moves with a constant velocity in $X-Y$ plane. Its possible angular momentum w.r.t. origin is

A particle of mass $m$ is moving with constant velocity $v$ parallel to the $x$-axis as shown in the figure. Its angular momentum about origin $O$ is ……….