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(C) The theorem of parallel axes is given by the equation $I = I_g + Md^2$,where $I$ is the moment of inertia about an axis parallel to the axis passi

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(C) The theorem of parallel axes is given by the equation $I = I_g + Md^2$,where $I$ is the moment of inertia about an axis parallel to the axis passing through the center of mass,$I_g$ is the moment of inertia about the center of mass,$M$ is the mass of the body,and $d$ is the perpendicular distance between the two axes.This equation is of the form $y = mx^2 + c$,where $y = I$,$x = d$,$m = M$,and $c = I_g$.Since $M$ is a positive constant,this represents a parabola that is symmetric about the $I$-axis.At $d = 0$,the value of $I$ is $I_g$,which is a non-zero positive constant. Therefore,the graph does not pass through the origin $(0, 0)$ but intersects the $I$-axis at $I = I_g$.Comparing this with the given options,graph $C$ represents a parabola that is symmetric about the $I$-axis and has a positive intercept on the $I$-axis,which matches the physical requirements.

Column-$I$	Column-$II$
$(1)$ Perpendicular Axis Theorem	$(a)$ $I = I_C + Md^2$
$(2)$ Parallel Axis Theorem	$(b)$ $I_z = I_x + I_y$

According to the theorem of parallel axes $I = I_g + Md^2$,the graph between $I$ and $d$ will be

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Match Column-$I$ with Column-$II$:
Column-$I$ Column-$II$
$(1)$ Perpendicular Axis Theorem $(a)$ $I = I_C + Md^2$
$(2)$ Parallel Axis Theorem $(b)$ $I_z = I_x + I_y$

Where, $d =$ distance between two parallel axes.

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