Question

A particle of mass $m$ moves in $xy$ plane along the line $y=x-4,$ with constant speed $v$, the angular momentum of particle about origin at any instant of time $t.$ is $x\sqrt{2}mv$. Find $x$.

Answer 1

$r_{\perp }=\frac{4}{\sqrt{2}}=2\sqrt{2}$
$L=mv{r}_{\perp }=2\sqrt{2}mv$
$2\sqrt{2}mv$