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Q.

The angular frequency of a fan increases from 30 rpm to 60 rpm in $π s$ . A dust particle is present at a distance of 20 cm from axis of rotation. The tangential acceleration of the particle in $π s$ is

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a

0 .8 {ms}^{- 2}

b

0.34 {ms}^{- 2}

c

0.2 {ms}^{- 2}

d

1.2 {ms}^{- 2}

answer is C.

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Detailed Solution

ω_{1} = 30 \times \frac{2 π}{60} = π

$ω_{2} = 60 \times \frac{2 π}{60} = 2 π, t = π s$

$r = 20 \times 10^{- 2} {m, a}_{t} = ?$

$a_{t} = r α$

$α = \frac{ω_{2} - ω_{1}}{t} = 1$

$a_{t} = 0.2 \times 1 = 0.2 {m/s}^{2}$

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The angular frequency of a fan increases from 30 rpm to 60 rpm in πs . A dust particle is present at a distance of 20 cm from axis of rotation. The tangential acceleration of the particle in πs is