Which of the following statement is false for the angular momentum \[\vec{L}\] about the origin ?
[JEE Main Solved Paper-2016 ]
A) \[\vec{L}=\frac{m\upsilon }{\sqrt{2}}R\hat{k}\]when the particle is moving from D to A
B) \[\vec{L}=-\frac{m\upsilon }{\sqrt{2}}R\hat{k}\] when the particle is moving from to B
C) \[\vec{L}=m\upsilon \left[ \frac{R}{\sqrt{2}}-a \right]\hat{k}\]when the particle is moving from C to D
D) \[\vec{L}=m\upsilon \left[ \frac{R}{\sqrt{2}}+a \right]\hat{k}\]when the particle is moving from B to C
Correct Answer: A , C
Solution :
\[\vec{L}=\vec{r}\times \vec{P}\]or\[\vec{L}=rp\sin \theta \hat{n}\]or\[\vec{L}={{r}_{\bot }}(P)\hat{n}\] For D to A\[\vec{L}=\frac{R}{\sqrt{2}}mV(-\hat{k})\] For A to B\[\vec{L}=\frac{R}{\sqrt{2}}mV(-\hat{k})\] For C to D\[\vec{L}=\left( \frac{R}{\sqrt{2}}+a \right)mV(\hat{k})\] For B to C\[\vec{L}=\left( \frac{R}{\sqrt{2}}+a \right)mV(\hat{k})\]Solution :
\[\vec{L}=\vec{r}\times \vec{P}\]or\[\vec{L}=rp\sin \theta \hat{n}\]or\[\vec{L}={{r}_{\bot }}(P)\hat{n}\] For D to A\[\vec{L}=\frac{R}{\sqrt{2}}mV(-\hat{k})\] For A to B\[\vec{L}=\frac{R}{\sqrt{2}}mV(-\hat{k})\] For C to D\[\vec{L}=\left( \frac{R}{\sqrt{2}}+a \right)mV(\hat{k})\] For B to C\[\vec{L}=\left( \frac{R}{\sqrt{2}}+a \right)mV(\hat{k})\]
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