A plane lamina with constant density occupies a region in the xy-plane bounded by a simple closed path C.Its moments of inertia about the axes are Find the moments of inertia about the axes,if C is a rectangle with vertices (0,0),(4,0), (4,5)and

Question

A plane lamina with constant density  occupies a region in the xy-plane bounded by a simple closed path C.Its moments of inertia about the axes are  Find the moments of inertia about the axes,if C is a rectangle with vertices (0,0),(4,0), (4,5)and

Quizplus · Accepted Answer

For a rectangle with vertices (0,0),(a,0), (a,b) and (0,b), the moments of inertia about the x-axis and y-axis are given by:
$I_x = \frac{1}{12} ab^3$ and $I_y = \frac{1}{12} a^3b$
Substituting $a=4$ and $b=5$, we get:
$I_x = \frac{1}{12} (4)(5^3) = \frac{125}{3}$
$I_y = \frac{1}{12} (4^3)(5) = 20$
Therefore, the answer is A) 11ea8a3b_b744_e355_9fff_174d03151c5c_TB6897_11.

A Plane Lamina with Constant Density Occupies a Region