Two Rods Of Equal Mass M And Length L Lie Along The X-axis And Y Axis With Their Centres Origin. What Is The Moment Of Inertia Of Both About The Line X=Y?

Sol:

Moment of inertial of a rod of about an axis passing through centre and perpendicular to a length:

[latex]I = \frac{MI^{2}}{I2}[/latex]

Moment of inertia of the rod about an axis inclined an angle θ to the original axis:

[latex]I’ = I sin^{2} \Theta [/latex]

The line x = y makes an angle of 45° about x and y axes.

Hence [latex] I’ = I sin^{2} 45 = \frac{I}{2}[/latex]

The moment of inertia of both rods about the line passing through x = y

[latex]I_{two/rods} = 2I'[/latex]

=[latex] 2 * \frac{I}{2} = I[/latex]

= [latex]\frac{MI^{2}}{I2}[/latex]

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