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Physics-

General

Easy

Question

A particle of mass $m$ moves in the $X Y$ plane with a velocity $v$ along the straight line $A B$ . If the angular momentum of the particle with respect to origin $O$ is $L subscript A end subscript$ when it is at $A$ and $L subscript B end subscript$ when it is at $B$ , then

$L_{A} > L_{B}$
$L_{A} = L_{B}$
The relationship between $L_{A}$ and $L_{B}$ depends upon the slope of the line $A B$
$L_{A} < L_{B}$

The correct answer is: $L subscript A end subscript equals L subscript B end subscript$

From the definition of angular momentum,

$L equals r cross times p equals r m v sin invisible function application empty set left parenthesis negative stack k with hat on top right parenthesis$
Therefore, the magnitude of $L$ is
$L equals m v r sin invisible function application empty set equals m v d$
where $d equals r sin invisible function application empty set$ is the distance of closest approach of the particle to the origin. As $d$ is same for both the particles, hence $L subscript A end subscript equals L subscript B end subscript$ .

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