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Question

A particle moves along two paths AOB and AB of an arc (r=π m) 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 π3 sec in each way?

A
6 m/s and 12 m/s respectively
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B
2.5 m/s and π6 m/s respectively
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C
6 m/s and 2π m/s respectively.
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D
2 m/s and 4.5 m/s respectively
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Solution

The correct option is C 6 m/s and 2π m/s respectively.
Given: Time interval, Δt=π3 sec
In case of path AOB,
Distance covered, S=r+r=2r=2π m
So, average speed is given by
vavg=2ππ3=6 m/s

In case of path AB,
Distance covered, S=2πrθ360 m
S=2π×π×120360=2π23 m
So, average speed is given by
vavg=2π23×π3=2π m/s
Hence the average speed for paths AOB and AB is 6 m/s and 2π m/s respectively.

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