Q.
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) $L_{A} < L_{B}$
Explanation
(b) From the definition of angular momentum,
[image:7_image148.emf]
$\mathbf{L} = \mathbf{r} \times \mathbf{p} = rmv\sin{\varnothing( - \widehat{\mathbf{k}})}$
Therefore, the magnitude of $L$ is
$L = mvr\sin{\varnothing = mvd}$
where $d = r\sin\varnothing$ is the distance of closest approach of the particle to the origin. As $d$ is same for both the particles, hence $L_{A} = L_{B}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.