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Question

A particle is moving with constant speed in a circular path. Find the ratio of average velocity from θ=0 to θ=π2 to its instantaneous velocity at θ=π2.

A
2π
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B
22π
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C
22π
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D
223π
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Solution

The correct option is C 22π

We know that the displacement D=AB=2r
Average velocity vavg=Dt=2rt
Time taken to describe angle θ=π2,
t=θω=θrv=πr2v

By putting the value of t in vavg, we get
vavg=22vπ

Instantaneous velocity =v

Thus, the ratio of average velocity to instantaneous velocity =22π

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