Rotational Motion Question 64
Question: 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]
Options:
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} $
Show Answer
Answer:
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} $ .
