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 LA when it is at A and LB when it is at B , then

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 LA when it is at A and LB when it is at B , then (A) LA=LB (B) the relationship between LA and LB depends upon the slope of the line AB (C) LA < LB (D) LA > LB

Tardigrade Admin · Accepted Answer

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

Q. 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 $L_{A}$ when it is at $A$ and $L_{B}$ when it is at $B$ , then

$L_{A} = L_{B}$

the relationship between $L_{A}$ and $L_{B}$ depends upon the slope of the line AB

$L_{A} < L_{B}$

$L_{A} > L_{B}$

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

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 LA​ when it is at A and LB​ when it is at B , then

LA​=LB​

the relationship between LA​ and LB​ depends upon the slope of the line AB

LA​<LB​

LA​>LB​