Question

Question-5) [Total 20 points] A homogen trapezoid with total mass of M having dimensions of height L and sides length 2a and 2b [uniform mass density is \sigma=\frac{M}{\text { Area

}} \equiv \text { constant] } is placed in x - y plane as shown in the figure below. Find the moment of inertia ly of the system about the y-axis. (Hint: an infinitesimal small mass segment dm is chosen and its dimensions are shown in the figure.)

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5