When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many more rotations will it make before coming to rest?
A
24
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B
36
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C
18
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D
12
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Solution
The correct option is D 12 From third equation of angular motion ω2=ω20−2∝θ [Here, ω=ω02,θ=36×2π] ∴(ω02)2=ω20−2α×36×2π or 4×36πα=ω20−ω204 or 4×36πα=3ω204 or α=ω2016×12π .......(i) According to question again applying the third equation of angular motion ω2=ω20−2αθ [Here, ω=0] ∴0=(ω02)2−2×ω20⋅θ16×12π or θ=24π or θ=12×2π But 2π=1 cycle So, θ=12 cycle