Question

A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin
(a) is zero
(b) remains constant
(c) goes on increasing
(d) goes on decreasing.

Answer 1

(b) remains constant

For angular momentum, we have:
$$\begin{gathered} \overrightarrow{L}=m\left(\overrightarrow{r}\times \overrightarrow{v}\right) \\ \overrightarrow{v}=v\hat{i}\mathrm{and}\overrightarrow{r}=x\hat{i}\mathit{+}y\hat{j} \\ \mathrm{So}\mathit{,}\mathit{}\overrightarrow{L}\mathit{=}\mathit{-}mvy\hat{k} \end{gathered}$$
m, v and y are constant; therefore, angular momentum remains constant.