A) 64 unit in \[-\,\hat{k}\]direction
B) 64 unit in \[+\,\hat{k}\]direction
C) 64 unit in \[+\,\hat{j}\]direction
D) 64 unit in \[-\,\,\hat{i}\] direction.
Correct Answer: B
Solution :
Key Idea: Angular momentum \[\vec{L}=m(\vec{r}\times \vec{v})\]For a body of mass m rotating with velocity v in a circle of radius r, the angular momentum is given by \[\vec{L}=m\,(\vec{r}+\vec{v})\] For unit mass \[m=1\] \[\therefore \] \[|\vec{L}|\,=(8\hat{i}-4\hat{j})\times (8\hat{i}+4\hat{j})\] \[|\vec{L}|\,=\,\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 8 & -4 & 0 \\ 8 & 4 & 0 \\ \end{matrix} \right|\] \[|\vec{L}|\,=\hat{i}(0-0)-\hat{j}(0-0)+\hat{k}(32+32)\] \[\Rightarrow \] \[|\vec{L}|=64\,k\,unit.\]
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