question_answer

                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:

A)                                                                                                                                                                                             \[{{L}_{A}}>{{L}_{B}}\]                 

B)                  \[{{L}_{A}}={{L}_{B}}\]

C)                  the relationship between \[{{L}_{A}}\] and \[{{L}_{B}}\] depends upon the slope of the line AB

D)                 \[{{L}_{A}}<{{L}_{B}}\]

Correct Answer: B

Solution :

                          From the definition of angular momentum,                 \[\vec{L}=\vec{r}\times \vec{p}=rmv\,\sin \,\phi \,\,(-\vec{k})\]                                 Therefore, the magnitude of L is                 \[L=mvr\sin \phi =mvd\]                 where \[d=r\sin \phi \] is the distance of closest approach of the particle to the origin. As d is same for both the particles, hence \[{{L}_{A}}={{L}_{B}}\].