A fly wheel rotating about a fixed axis has a kinetic energy of 360 joule when its angular speed is 30…

A fly wheel rotating about a fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec. The moment of inertia of the wheel about the axis of rotation is
  1. $0.6 \mathrm{~kg} / \mathrm{m}^{2}$
  2. $0.15 \mathrm{~kg} \mathrm{~m}^{2}$
  3. $0.8 \mathrm{~kg} \mathrm{~m}^{2}$
  4. $0.75 \mathrm{~kg} \mathrm{~m}^{2}$

Solution

$E_{r}=\frac{1}{2} I \omega^{2} \Rightarrow$
$I=\frac{2 E_{r}}{\omega^{2}}=\frac{2 \times 360}{30 \times 30}=0.8 \mathrm{~kg} \mathrm{~m}^{2}$ ^

Asked in: JEE Mains - Rotational Motion - Test 2

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