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
2√2π
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D
2√23π
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Solution
The correct option is C2√2π
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=2√2vπ
Instantaneous velocity =v
Thus, the ratio of average velocity to instantaneous velocity =2√2π