Question

A mass $m$ is moving with a constant velocity $v$ along a line parallel to $X-$ axis, away from origin. Then, its angular momentum with respect to the origin

• A. is zero
• B. remains constant
• C. goes on increasing
• D. goes on decreasing

Answer 1

The correct option is B remains constant

Particle is moving with a constant velocity $\overrightarrow{v}$ parallel to $X-$axis, then the position vector $\overrightarrow{r}$ of particle is changing with respect to origin, but not the perpendicular distance about origin $O$.

$\Rightarrow \perp$ distance of particle about origin$=\text{constant}=y$
$\Rightarrow$Angular momentum about $O$:
$|\overrightarrow{L}|=mv{r}_{\perp }=mvy$
$\therefore |\overrightarrow{L}|=\text{constant}$
Direction of $\overrightarrow{L}$ is governed by direction of $(\overrightarrow{r}\times m\overrightarrow{v})$, so it is also constant, since $\overrightarrow{L}$ is coming along $-veZ$-axis, i.e perpendicularly inwards for the plane $X-Y$.