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:                     [AIPMT (S) 2007]

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