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