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## Homework Statement

Two uniform square laminas are combined into a single body. One lamina ABCD has mass 5m and the other lamina PQRS has mass m. The lamina PQRS has side 2a, and its vertices are at the mid-points of the sides of ABCD, with P on AB and S on AD. The line PS meets AC at K, and the body rotates in a vertical plane about a horizontal axis k through K (see diagram). Find the moment of inertia of the body about k.

## Homework Equations

parallel and the perpendicular axes theorems

## The Attempt at a Solution

If i understand the question correctly, is the "dashed"(broken)line, the axis about which we need to find the moment of inertia ? If that is the case, here is what i did :Using the perpendicular axes theorem : (let [itex]I_{A}[/itex] be the moment of inertia about the required axis for ABCD only)

2[itex]I_{A}[/itex] = [itex]\frac{5m(2a^{2}+2a^{2})}{3}[/itex]

[itex]I_{A}[/itex] = [itex]\frac{10ma^{2}}{3}[/itex]

Similarly, let [itex]I_{B}[/itex] be the moment of inertia about the required axis for PQRS only :

Using the perpendicular axes theorem,

[itex]I_{B}[/itex] = [itex]\frac{ma^{2}}{3}[/itex]

The total moment of inertia = [itex]I_{A}[/itex] + [itex]I_{B}[/itex]

Total = [itex]\frac{11ma^{2}}{3}[/itex]

The problem is that the solution notes state the answer to be [itex]\frac{40ma^{2}}{3}[/itex]