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

Question

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 (A) 1600 ms-2 (B) 47.4 ms-2 (C) 23.7 ms-2 (D) 50.55 ms-2

Tardigrade Admin · Accepted Answer

Frequency of rotation v=120 rpm =2 rps length of blade r=30 cm =0.3 m Centripetal acceleration a=ω2 r=(2 π v)2 r =4 π2 v2 r=4 π2(2)2(0.3)=47.4 ms -2

Q. An electric fan has blades of length $30 c m$ measured from the axis of rotation. If the fan is rotating at $120 r p m$ , the acceleration of a point on the tip of the blade is

$1600 m s^{- 2}$

$47.4 m s^{- 2}$

$23.7 m s^{- 2}$

$50.55 m s^{- 2}$

Frequency of rotation $v = 120 r p m = 2 r p s$
length of blade $r = 30 c m = 0.3 m$
Centripetal acceleration $a = ω^{2} r = (2 π v)^{2} r$
$= 4 π^{2} v^{2} r = 4 π^{2} (2)^{2} (0.3) = 47.4 m s^{- 2}$

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

1600ms−2

47.4ms−2

23.7ms−2

50.55ms−2