Question

A particle of mass $m$ moves in the $XY$ plane with a velocity ' $v$ ' along the straight line $A B$. 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. $L_{A} < L_{B}$

Answer 1

Answer: (B)

From the definition of angular momentum,
$\vec{ L }=\vec{ r } \times \vec{ p }=r m v \sin \phi(-\hat{ k })$

Therefore, the magnitude of $L$ is
$L=m v r \sin \phi=m v d$
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 $L_{A}=L_{B}$.