Assertion : Moment of inertia depends on the | vedclass

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Question

(B) The moment of inertia $I$ of a system of particles is defined as $I = \sum m_i r_i^2$,where $r_i$ is the perpendicular distance of the $i$-th part

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If both $Assertion$ and $Reason$ are correct but $Reason$ is not a correct explanation of the $Assertion$.

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(B) The moment of inertia $I$ of a system of particles is defined as $I = \sum m_i r_i^2$,where $r_i$ is the perpendicular distance of the $i$-th particle of mass $m_i$ from the axis of rotation.From this definition,it is clear that $I$ depends on the distribution of mass relative to the axis of rotation and the position/orientation of the axis itself. Thus,the $Assertion$ is correct.$Moment$ of inertia is defined as the rotational analogue of mass in linear motion. Just as mass represents the inertia of a body in linear motion (resistance to change in linear velocity),the moment of inertia represents the rotational inertia of a body (resistance to change in angular velocity). Thus,the $Reason$ is also correct.However,the $Reason$ explains what the moment of inertia represents (rotational inertia),but it does not explain *why* it depends on the axis of rotation and mass distribution. Therefore,the $Reason$ is not the correct explanation of the $Assertion$. The correct option is $B$.

Column $I$	Column $II$
$(A)$ 'k' for a solid sphere rotating about its tangent	$(P)$ $\sqrt{2}R$
$(B)$ 'k' for a ring rotating about its tangent perpendicular to its plane	$(Q)$ $\frac{R}{2}$
$(C)$ 'k' for a uniform solid right circular cone rotating about its central axis	$(R)$ $\frac{\sqrt{7}}{\sqrt{5}}R$
$(D)$ 'k' for a uniform disc rotating about its diameter	$(S)$ $\frac{\sqrt{3}}{\sqrt{10}}R$

$Assertion$ : Moment of inertia depends on the axis of rotation and the nature of distribution of the mass of the body.
$Reason$ : Moment of inertia is the rotational inertia of the body.

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$Assertion$ : Moment of inertia depends on the axis of rotation and the nature of distribution of the mass of the body.$Reason$ : Moment of inertia is the rotational inertia of the body.