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

Step-by-step solution

From the definition of angular momentum, L = r × p = r m v sin ⁡ ∅ ( - k ^ ) Therefore, the magnitude of L is L = m v r sin ⁡ ∅ = m v d where d = r sin ⁡ ∅ 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 .