Consider the following statements:Assertion ( | vedclass

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(B) According to the parallel axis theorem,the moment of inertia $I$ about any axis is given by $I = I_{cm} + Md^2$,where $I_{cm}$ is the moment of in

Vedclass · Accepted Answer

Both $A$ and $R$ are true but $R$ is not a correct explanation of $A$.

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(B) According to the parallel axis theorem,the moment of inertia $I$ about any axis is given by $I = I_{cm} + Md^2$,where $I_{cm}$ is the moment of inertia about the parallel axis passing through the centre of mass,$M$ is the mass of the body,and $d$ is the perpendicular distance between the two axes.Since $Md^2$ is always non-negative,$I$ is minimum when $d = 0$,which means the axis passes through the centre of mass. Thus,Assertion $(A)$ is true.In a uniform gravitational field,the weight of a body acts through its centre of mass. Thus,Reason $(R)$ is true.However,the fact that weight acts through the centre of mass is a property related to gravity and does not explain why the moment of inertia is minimum about the centre of mass axis (which is a geometric property derived from the parallel axis theorem). Therefore,$R$ is not the correct explanation of $A$.

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