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  4. This question has Statement land Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: When moment of inertia I of a body rotating about an axis with angular speed co increases, its angular momentum L is unchanged but the kinetic energy K increases if there is no torque applied on it. Statement 2: L = Iω, kinetic energy of rotation = (1/2)Iω2

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Q. This question has Statement land Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: When moment of inertia I of a body rotating about an axis with angular speed co increases, its angular momentum L is unchanged but the kinetic energy K increases if there is no torque applied on it.
Statement 2: $L = I\omega$, kinetic energy of rotation $ = \frac{1}{2}I\omega^{2}$

AIEEEAIEEE 2012

Solution:

As $L = I\omega$ so L increases with increase in co. Kinetic energy$_{(rotational)}$ depends on an angular velocity $\omega$ of and moment of inertia of the body I.
$i.e., \,K.E._{\left(rotational\right)} = \frac{1}{2}I\omega^{2}$