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Physics Question on Motion in a plane

An insect trapped in a circular groove of radius 12 cm12\,cm moves along the groove steadily and completes 77 revolutions in 100 s100\,s. The linear speed of the insect is

A

4.3 cms−14.3\,cms^{-1}

B

5.3 cms−15.3\,cms^{-1}

C

6.3 cms−16.3\,cms^{-1}

D

7.3 cms−17.3\,cms^{-1}

Answer

5.3 cms−15.3\,cms^{-1}

Explanation

Solution

Here, r=12 cmr = 12\, cm, frequency, υ=7100rps\upsilon=\frac{7}{100}rps The angular speed of the insect is ω=2πυ=2π×7100=0.44 rad s−1\omega=2\pi\upsilon=2\pi\times\frac{7}{100}=0.44\,rad\,s^{-1} The linear speed of the insect is v=ωr=0.44×12v= \omega r=0.44 \times 12 =5.3 cms−1 = 5.3\, cm s^{-1}