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GATE2020-ME-2: 29

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The sun (S) and the Planet (P) of an epicyclic gear train shown in the figure have identical number of teeth.

If the sun (S) and the outer ring (R) gears are rotated in the same direction with angular speed $\omega_S$ and $\omega_R$, respectively, then the angular speed of the arm $AB$ is

  1. $\dfrac{3}{4} \omega _R + \dfrac{1}{4} \omega _S \\$
  2. $\dfrac{1}{4} \omega _R + \dfrac{3}{4} \omega _S \\$
  3. $\dfrac{1}{2} \omega _R - \dfrac{1}{2} \omega _S \\$
  4. $\dfrac{3}{4} \omega _R - \dfrac{1}{4} \omega _S $
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