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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 Lᵦ when it is at B, then:

1. Lₐ = Lᵦ
2. The relationship between Lₐ and Lᵦ depends upon the slope of the line AB
3. Lₐ < Lᵦ
4. Lₐ > Lᵦ

Correct answer: Lₐ = Lᵦ

Solution

Angular momentum of a particle about a point is given by the cross product of its position vector and linear momentum. Since the particle moves along a straight line and the origin does not change, the perpendicular distance from the origin to the line remains constant, making the angular momentum constant. Thus, Lₐ = Lᵦ.

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