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(A) The angular momentum $L$ of a particle with respect to an origin $O$ is given by the formula $L = r 	imes p = r 	imes (mv),$ where $r$ is the po

Vedclass · Accepted Answer

$L_A = L_B$

Vedclass · Answer

(A) The angular momentum $L$ of a particle with respect to an origin $O$ is given by the formula $L = r 	imes p = r 	imes (mv),$ where $r$ is the position vector of the particle and $p$ is its linear momentum.This can also be expressed as $L = m v d,$ where $d$ is the perpendicular distance from the origin $O$ to the line of motion of the particle.Since the particle is moving along a straight line $AB,$ the perpendicular distance $d$ from the origin $O$ to this line remains constant at all points on the line.Therefore,the angular momentum $L$ is constant for all points on the line $AB.$Thus,$L_A = L_B.$

$A$ 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

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