A Plane Lamina with Constant Density $\rho ( x , y ) = 12$

question 86

Multiple Choice

A plane lamina with constant density $\rho ( x , y ) = 12$ occupies a region in the xy-plane bounded by a simple closed path C. Its moments of inertia about the axes are $I _ { x } = - \frac { \rho } { 3 } \int _ { C } y ^ { 3 } d x \text { and } I _ { y } = \frac { \rho } { 3 } \int _ { C } x ^ { 3 } d y$ Find the moments of inertia about the axes, if C is a rectangle with vertices (0, 0) , (4, 0) , (4, 5) and $( 0,5 )$ .

• A) \(( - 1,280,1,280 )\)
• B) \(( - 2,880,1,200 )\)
• C) \(( 2,000 , - 1,280 )\)
• D) \(( 2000,1280 )\)
• E) \(( - 2,000,1,280 )\)

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