If two particles are moving on same circle with different angular velocities $ω_{1}$ and $ω_{2}$ , and different time periods $T_{1}$ and $T_{2}$ , then the time taken by the particle 2 to complete one revolution with respect to particle 1 is

T = \frac{T_{1} T_{2}}{T_{2} - T_{1}}

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T = \frac{T_{1} + T_{2}}{2}

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T = \frac{T_{1} T_{2}}{T_{2} + T_{1}}

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T = T_{2} - T_{1}

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Solution

The correct option is C $T = \frac{T_{1} T_{2}}{T_{2} + T_{1}}$
Case-(i): Both moving in same direction
Relative angular velocity is given by $ω_{2} - ω_{1}$
$T = \frac{2 π}{ω_{2} - ω_{1}}$
$= \frac{2 π}{\frac{2 π}{T_{2}} - \frac{2 π}{T_{1}}}$
$= \frac{T_{1} T_{2}}{T_{1} - T_{2}}$
Case-(ii): Both moving in opposite direction.
Relative angular velocity is given by
$ω_{2} + ω_{1}$
$T = \frac{2 π}{ω_{2} + ω_{1}}$
$= \frac{2 π}{\frac{2 π}{T_{2}} + \frac{2 π}{T_{1}}}$
$= \frac{T_{1} T_{2}}{T_{1} + T_{2}}$

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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

If two particles are moving on same circle with different angular velocities $ω_{1}$ and $ω_{2}$ , and different time periods $T_{1}$ and $T_{2}$ , then the time taken by the particle 2 to complete one revolution with respect to particle 1 is