question_answer

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) \[{{L}_{A}}>{{L}_{B}}\]

C) \[{{L}_{A}}<{{L}_{B}}\]

D) The relationship between \[{{L}_{A}}\]and \[{{L}_{B}}\] depends upon the slope of the line AB           

Correct Answer: A

Solution :

Angular momentum = linear momentum x distance of line of action of linear momentum about the origin. \[{{L}_{A}}={{P}_{A}}\times d\] and \[{{L}_{B}}={{P}_{B}}\times d\] As linear momenta are equal, therefore, \[{{L}_{A}}={{L}_{B}}\].