A particle of mass $20\,g$ is released with an initial velocity $5\,m/s$ along the curve from the point $A,$ as shown in the figure. The point $A$ is at height $h$ from point $B.$ The particle slides along the frictionless surface. When the particle reaches point $B,$ its angular momentum about $O$ will be ......... $kg - m^2/s$. [Take $g = 10\,m/s^2$ ]

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 .......

A particle of mass $M=0.2 kg$ is initially at rest in the $x y$-plane at a point $( x =-l, y =-h)$, where $l=10 m$ and $h=1 m$. The particle is accelerated at time $t =0$ with a constant acceleration $a =10 m / s ^2$ along the positive $x$-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $\vec{L}$ and $\vec{\tau}$, respectively. $\hat{i}, \hat{j}$ and $\hat{k}$ are unit vectors along the positive $x , y$ and $z$-directions, respectively. If $\hat{k}=\hat{i} \times \hat{j}$ then which of the following statement($s$) is(are) correct?

$(A)$ The particle arrives at the point $(x=l, y=-h)$ at time $t =2 s$.

$(B)$ $\vec{\tau}=2 \hat{ k }$ when the particle passes through the point $(x=l, y=-h)$

$(C)$ $\overrightarrow{ L }=4 \hat{ k }$ when the particle passes through the point $(x=l, y=-h)$

$(D)$ $\vec{\tau}=\hat{ k }$ when the particle passes through the point $(x=0, y=-h)$

Obtain the relation between angular momentum of a particle and torque acting on it. 

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