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
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B
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C
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D
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Solution

## The correct option is A 4 rad/sPosition 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) →vB−→vA=−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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