Two identical thin rods of mass M ~kg and length L ~m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is x 12 ML ² ~kg ~m ² . Th

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Two identical thin rods of mass M ~kg and length L ~m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is x 12 ML ² ~kg ~m ² . The value of x is _ _ _ _ .

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For vertical rod with axis at end P: I₁ = ML^2 3 For horizontal rod centered at distance L from P: I₂ = _ -L/2 ^ L/2 M L (x^2 + L^2)dx = M L [ x^3 3 + L^2x ]_ -L/2 ^ L/2 = M L [ L^3 12 + L^3 ] = 13ML^2 12 Total: I = ML^2 3 + 13ML^2 12 = 4ML^2 + 13ML^2 12 = 17ML^2 12 x = 17

Two identical thin rods of mass M ~kg and length L ~m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is x 12 ML ² ~kg ~m ² . The value of x is _ _ _ _ .

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