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Two particles each of mass m and velocity v are travelling in the same direction along two parallel lines, in the plane of the paper, separated by a distance d. A and B are two points on their lines of motion and C is a point midway between the two lines (as shown in the figure). Read the following statements  The magnitude of the total angular momentum of the two-particle system around the point A will be mvd  The magnitude of the total angular momentum of the system around the point B will be mvd  The magnitude of the vector sum of angular momenta of the system around points A and B shal be zero  The magnitude of the angular momentum of the system around C will be zero Which of the above statements is/are correct?

A)  (i) and (ii) only                 

B)  (iii) only

C)  (iii) and (iv) only              

D)  (i), (ii), (iii) and (iv)

Correct Answer: D

Solution :

                 We know that L = mrv = mvd Hence, the magnitude of the total angular momentum of the two-particle system around the point A will be mvd. Similarly the magnitude of total angular momentum of the system around the point B will be mvd. The magnitude of the vector sum\[L={{L}_{1}}+{{L}_{2}}=mvd-mvd=0\] The magnitudes of the angular momentum of the system around C                 \[L=mvd\]                           \[(\because \,d=0)\] \[\therefore \]  \[L=0\]