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

• A. $L_A=L_B$
• B. the relationship between $L_A$ and $L_B$ depends upon the slope of the line AB
• C. $L_A < L_B$
• D. $L_A > L_B$

Answer 1

Answer: (A)

$\vec{ L }=\vec{ r } \times \vec{ P } $
or $\vec{ L }=\vec{ r } \times m \vec{ V }$
Where $\vec{ V }$ is velocity vector and we know that it is same at both points $A$ and $B$.
$\vec{r}$ is perpendicular vector on the velocity vector from origin that is perpendicular on line $AB$ so $\vec{r}$ is also same in both cases .
So $L _{ A }= L _{ B }$