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An electric fan has blades of length 30 cm measured from the axis of rotation. If the fan is rotating at 120 rpm, the acceleration of a point on the tip of the blade is

1. 1600 m/s²
2. 47.4 m/s²
3. 23.7 m/s²
4. 50.55 m/s²

Correct answer: 47.4 m/s²

Solution

The angular velocity is calculated as \( \omega = \frac{2\pi \times 120}{60} = 4\pi \) rad/s. The centripetal acceleration is \( a = \omega^2 r \), where \( r = 0.3 \) m. Substituting, \( a = (4\pi)^2 \times 0.3 = 47.4 \) m/s².

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