Question

A particle of mass $m$ is moving with a constant velocity $v$ parallel to the $x-$ axis as shown in the figure. Its angular momentum (magnitude) about origin $\text{O}$ is

• A. $mvb$
• B. $mva$
• C. $mv\sqrt{a^2+b^2}$
• D. $mv(a+b)$

Answer 1

The correct option is A $mvb$

Given, velocity of particle $=v\hat{i}$
Position vector w.r.t. origin $\overrightarrow{r}=(a-0)\hat{i}+(b-0)\hat{j}$
$\overrightarrow{r}=a\hat{i}+b\hat{j}$
Angular momentum $\overrightarrow{L}=m(\overrightarrow{r}\times \overrightarrow{v})$
$\overrightarrow{L}=m[(a\hat{i}+b\hat{j})\times \left(v\hat{i}\right)]$
$\overrightarrow{L}=m\left(bv\right)(-\hat{k})$
$\overrightarrow{L}=mbv(-\hat{k})$