A rigid body can be hinged about any point on the x-axis. When the hinge is at coordinate x, its moment of inertia is I = 2x² - 12x + 27. The x-coordinate of the centre of mass is:
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Question

A rigid body can be hinged about any point on the x-axis. When the hinge is at coordinate x, its moment of inertia is I = 2x² - 12x + 27. The x-coordinate of the centre of mass is:

G1 Physics · Accepted Answer

By the parallel-axis theorem, I(x)=I about CM + M(x-x of CM)². Therefore I(x) is minimum when the hinge passes through the centre of mass. For I=2x²-12x+27, dI/dx=4x-12=0, giving x=3. Hence option D.