Dear student, For rod along x- axis, I1=13ML2 For rod along y- axis, â€‹I2=Mr2=ML22=14ML2 For rod along z- axis, â€‹I3=Ic+Mr2=112ML2+ML22=112ML2+14ML2Itotal=I1+I2+I3=13ML2+14ML2+112ML2+14ML2=1112ML2 Regards

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Dear student,

For rod along x- axis,

I_{1} = \frac{1}{3} M L^{2}

For rod along y- axis,

I_{2} = M r^{2} = M {(\frac{L}{2})}^{2} = \frac{1}{4} M L^{2}

For rod along z- axis,

I_{3} = I_{c} + M r^{2} = \frac{1}{12} M L^{2} + M {(\frac{L}{2})}^{2} = \frac{1}{12} M L^{2} + \frac{1}{4} M L^{2} I_{t o t a l} = I_{1} + I_{2} + I_{3} = \frac{1}{3} M L^{2} + \frac{1}{4} M L^{2} + \frac{1}{12} M L^{2} + \frac{1}{4} M L^{2} = \frac{11}{12} M L^{2}

Regards.

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