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Q.

A stationary wheel starts rotating about its own axis at constant angular acceleration. If the wheel completes 50 rotations in first 2 seconds, then the number of rotations made by it in next two seconds is

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a

75

b

100

c

125

d

150

answer is D.

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Detailed Solution

$\begin{array}{l} ω_{i} = 0; t = 2 s \\ θ = 50 (2 π) = 100 πrad \\ ∴ α = \frac{2 θ}{t^{2}} = \frac{200 π}{4} = 50 {πrads}^{- 2} \\ ' θ' in 4 \sec; θ = \frac{1}{2} {αt}^{2} = \frac{1}{2} (50 π) (16) \\ = 400 π rad \\ in the last 2 \sec, θ = 400 π - 100 π = 300 πrad \\ ∴ no . of rotations = \frac{θ}{2 π} = \frac{300 π}{2 π} = 150 \end{array}$

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