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Question: An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes...

An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100 s. The linear speed of the insect is

A

4.3cms−14.3cms^{- 1} (4.3 cm/s)

B

5.3cms−15.3cms^{- 1} (5.3 cm/s)

C

6.3cms−16.3cms^{- 1} (6.3 cm/s)

D

7.3cms−17.3cms^{- 1} (7.3 cm/s)

Answer

5.3cms−15.3cms^{- 1} (5.3 cm/s)

Explanation

Solution

Here, r = 12cm

Frequency, u=7100Hzu = \frac{7}{100}Hz

The angular speed of the insect is

ω=2πυ=2π×7100=0.44rads−1\omega = 2\pi\upsilon = 2\pi \times \frac{7}{100} = 0.44rads^{- 1}

The linear speed of the insect is

v=ωr=0.44×12=5.3cms−1v = \omega r = 0.44 \times 12 = 5.3cms^{- 1}