A particle of mass \(m\) moves in the \(XY\)-plane with a velocity \(v\) along the straight line....

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A particle of mass \(m\) moves in the \(XY\)-plane with a velocity \(v\) along the straight line \(AB\). If the angular momentum of the particle with respect to origin \(O\) is \(L _{ A }\) when it is at \(A\) and \(L _{ B }\) when it is at \(B\), then
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