Q32 / 122 · NTA Abhyas (JEE Main) 2020 · Physics · Rotational Motion

When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many rotations will it make before coming to rest?

  • A
    24
  • B
    36
  • C
    18
  • Correct answer
    D
    12

Solution

From the third equation of angular motion,

ω2=ω02-2αθ  (Here,ω=ω02,θ=36×2π)

∴ ω022=ω02-2α×36×2π

or 4×36πα=ω02-ω024

or 4×36πα=3ω024

or α=ω0216×12π ...(i)

According to question again applying the third equation of angular motion

ω2=ω02-2αθ                     (Here, ω=0)

∴ 0=ω022-2×ω02.θ16×12π

or θ=24π        or       θ=12×2π

But 2π=1 cycle

So, θ=12 cycle

Hence, the correct answer is option: 'D'.

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