The moment of inertia of a solid sphere about | vedclass

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(D) The moment of inertia of a solid sphere about its diameter is given by $I_{cm} = \frac{2}{5}MR^2$,where $M$ is the mass and $R$ is the radius of t

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(D) The moment of inertia of a solid sphere about its diameter is given by $I_{cm} = \frac{2}{5}MR^2$,where $M$ is the mass and $R$ is the radius of the sphere.According to the parallel axis theorem,the moment of inertia $I$ about an axis at a distance $x$ from the diameter is given by $I = I_{cm} + Mx^2$.Substituting the value of $I_{cm}$,we get $I = \frac{2}{5}MR^2 + Mx^2$.This equation is of the form $I = Mx^2 + C$,where $C = \frac{2}{5}MR^2$ is a constant.This represents a parabola that opens upwards with its vertex at $(0, \frac{2}{5}MR^2)$,which corresponds to the graph shown in option $D$.

The moment of inertia of a solid sphere about an axis parallel to its diameter and at a distance $x$ from it is represented by $I$. Which of the following graphs shows the variation of $I$ with $x$?

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