A right body can be hinged about any point on the x-axis. When it is hinged such that the hinge is at x, the moment of inertia is given by $I = 2 x^{2} - 12 x + 27$ . The x coordinate of center of mass at x is ____

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answer is 3.

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Detailed Solution

Moment of inertia is minimum at the location of center of mass

So, $\frac{dI}{dx} = 0, 4 x - 12 = 0 \Rightarrow x = 3$

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