Question

If a particle of mass m is moving with constant velocity $V$ parallel to $X-$ axis in $XY$ plane at a distance $y$. Then its angular momentum at any time ${}^{\prime }{t}^{\prime }$ with respect to the origin is :

• A. $-mcy$ $\overrightarrow{i}$
• B. $-mvy$ $\overrightarrow{j}$
• C. $-mvy$ $\overrightarrow{k}$
• D. $mvy$ $\overrightarrow{k}$

Answer 1

Answer: (C)

$-mvy$ $\overrightarrow{k}$

The position vector is given as,

$\overrightarrow{r}=y\hat{j}$

The velocity of the body is given as,

$\overrightarrow{v}=v\hat{i}$

The angular momentum is given as,

$\overrightarrow{L}=m\left(\overrightarrow{r}\times \overrightarrow{v}\right)$

$\overrightarrow{L}=m\left(y\hat{j}\times v\hat{i}\right)$

$\overrightarrow{L}=-myv\hat{k}$

Thus, the angular momentum with respect to origin is $-myv\hat{k}$.