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A ring type fly wheel of mass 100kg and diameter 2m is rotating at the rate of (300/π) revolutions per minute .Then

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a

The moment of inertia of the flywheel is 100 kgm²

b

The moment of inertia of the fly wheel is 143 kgm²

c

The kinetic energy of rotation of the flywheel is 5kJ.

d

The fly wheel , if subjected to a rotating torque of 200Nm will come to rest in 5s.

answer is A, B, C.

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Detailed Solution

Moment of inertia = MR²
$\begin{array}{l} = 10 \times 1 \times 1 \\ = 100 {kgm}^{2} \end{array}$
Energy of rotation $= \frac{1}{2} \times 100 \times {[2 π \times \frac{300}{π \times 60}]}^{2} = 5 k J$
$\begin{array}{l} \Rightarrow ω_{0} = 2 π \times \frac{300}{π \times 60} \\ ω = 0 \\ α = \frac{200}{100} rad / \sec^{2} \\ Now, ω = ω_{0} - αt, t = 5 \sec \end{array}$

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