A) \[mvb\,\hat{k}\]
B) \[-mvb\,\hat{k}\]
C) \[mvb\,\hat{i}\]
D) \[mv\,\hat{i}\]
Correct Answer: B
Solution :
We know that, Angular momentum \[\overrightarrow{L}=\overrightarrow{r\,}\times \overrightarrow{p}\] in terms of component becomes \[\overrightarrow{L}=\left| \,\begin{matrix} \hat{i}\,\, & \hat{j}\,\, & {\hat{k}} \\ x\,\, & y\,\, & z \\ {{p}_{x}} & \,\,{{p}_{y}}\,\, & {{p}_{z}} \\ \end{matrix}\, \right|\] As motion is in x-y plane (z = 0 and \[{{P}_{z}}=0\]), so \[\overrightarrow{L\,}=\overrightarrow{k\,}(x{{p}_{y}}-y{{p}_{x}})\] Here x = vt, y = b, \[{{p}_{x}}=m\,v\] and \[{{p}_{y}}=0\] \ \[\overrightarrow{L\,}=\overrightarrow{k\,}\left[ vt\times 0-b\,mv \right]=-mvb\,\hat{k}\]You need to login to perform this action.
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