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A wheel rotates with a constant acceleration of 2.0 radian/sec2. If the wheel starts from rest the number of revolutions it makes in the first ten seconds will be approximately
  • a)
    8
  • b)
    16
  • c)
    24
  • d)
    32
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A wheel rotates with a constant acceleration of 2.0 radian/sec2. If th...
Given, acceleration of the wheel, α = 2.0 rad/s²
Initial velocity, u = 0 (as the wheel starts from rest)
Time, t = 10 s
Let the final angular velocity of the wheel be ω.
Using the third equation of motion of rotational motion, we have:
ω = u + αt
ω = 0 + 2.0 × 10
ω = 20 rad/s
Let the number of revolutions made by the wheel in 10 seconds be n.
We know that the angular displacement, θ = ωt + 1/2 αt²
θ = 0 + 1/2 × 2.0 × 10²
θ = 100 rad

1 revolution = 2π rad
Therefore, the number of revolutions, n = θ/2π
n = 100/2π
n ≈ 15.92
Therefore, the wheel makes approximately 16 revolutions in the first ten seconds.
Hence, the correct option is (b) 16.
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