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 the origin O is L A when it is at A and L B 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 the origin O is L A when it is at A and L B 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 AB, L A L B

MARKS App · Accepted Answer

From the definition of angular momentum, L = r × p = r m v sin ⁡ ϕ ( - k ^ ) Therefore, the magnitude of L is L = m v r sin ⁡ ϕ = m v d where d = r sin ⁡ ϕ is the distance of closest approach of the particle to the origin. As d is same for both the particles, hence L A = L B .

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