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Question

Two particles A and B are moving in a horizontal place anticlockwise on two different concentric circles with different constant angular velocities 2ω and ω respectively. Find angular velocity (in rad/s) of B w.r.t. A after time t=πω. They both start at the position as shown in figure (Take ω=3 rad /sec,r=2 m)

A
4 rad/s
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B
5 rad/s
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C
16 rad/s
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D
25 rad/s
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Solution

The correct option is A 4 rad/s
Position of particle A after time t=πω,
θA=ωAt
=2ω×πω=2π
Position of particle B after time t=πω,
θB=ωBt
=ω×πω=π
Final position after time t=πω s are shown in figure.
Velocity of particle A, vA=2ωr(^j)
Velocity of particle B, vB=ω2r(^j)
vBvA=4ωr^j=4×3×2^j
=24^j m/s
Angular velocity of B w.r.t A, ωAB=vABAB=243(2)=|4|=4 rad/s

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