A particle moves along two paths AOB and AB of an arc (r=πm) as shown in the figure. What will be the average speed of particle for the paths AOB and AB respectively, if it completes the journey from A to B in π3sec in each way?
A
6m/s and 12m/s respectively
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B
2.5m/s and π6m/s respectively
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C
6m/s and 2πm/s respectively.
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D
2m/s and 4.5m/s respectively
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Solution
The correct option is C6m/s and 2πm/s respectively. Given: Time interval, Δt=π3sec In case of path AOB, Distance covered, S=r+r=2r=2πm So, average speed is given by vavg=2ππ3=6m/s
In case of path AB, Distance covered, S=2πrθ360∘m ⇒S=2π×π×120∘360∘=2π23m So, average speed is given by vavg=2π23×π3=2πm/s Hence the average speed for paths AOB and AB is 6m/s and 2πm/s respectively.