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

question 29

Multiple Choice

A plane lamina with constant density $\rho ( x , y ) = 12$ occupies a region in the $x y$ -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) \(( - 2,000,1,280 )\)