Question

# Two particles A and B are revolving with constant angular velocity on two concentric circles of radius 1m and 2m respectively as shown in figure. The positions of the particles at t=0 are shown in figure. If mA=2kg, mB=1kg and PA and PB are linear momentum of the particles then what is the maximum value of |PA+PB| in kgm/s in subsequent motion of the two particles. A
1
B
7
C
8
D
5
Solution
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#### Since the angular velocities of both the masses are constant, their linear velocities would also remain constant using the relation v=rω.Thus at each point their velocities change only in direction. Thus the momentum of particle A is PA=mAvA i.e. 2×2=4kgm/s and that of B is PB=mBvB i.e. 1×3=3kgm/s.We will get their momentum as a maximum when the particles travel parallel to each other in the same direction.Thus we get the maximum value of their momentum simply as the sum of their individual momentums i.e. |PA+PB|=4−3=1kgm/s at all points.

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