If two particles are moving on same circle with different angular velocities ω1 and ω2, and different time periods T1 and T2, then the time taken by the particle 2 to complete one revolution with respect to particle 1 is
A
T=T1T2T2−T1
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B
T=T1+T22
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C
T=T1T2T2+T1
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D
T=T2−T1
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Solution
The correct option is CT=T1T2T2+T1 Case-(i): Both moving in same direction
Relative angular velocity is given by ω2−ω1 T=2πω2−ω1 =2π2πT2−2πT1 =T1T2T1−T2 Case-(ii): Both moving in opposite direction.
Relative angular velocity is given by ω2+ω1 T=2πω2+ω1 =2π2πT2+2πT1 =T1T2T1+T2