A thin plate of uniform thickness is subject to pressure as shown in the figure below

Under the assumption of plane stress, which one of the following is correct?

The flexural rigidity $$(EI)$$ of a cantilever beam is assumed to be constant over the length of the beam as shown in figure. If a load $$P$$ and bending moment $$PL/2$$ are applied at the free end of the beam then the value of the slope at the free end is

A cantilever beam of length, $$L,$$ with uniform cross-section and flexural rigidity $$ EI,$$ is loaded uniformly by a vertical load, $$w$$ per unit length. The maximum vertical deflection of the beam is given by

Consider a flywheel whose mass $$M$$ is distributed almost equally between a heavy, ring-like rim of radius $$R$$ and a concentric disk-like feature of radius $$R/2$$. Other parts of the flywheel, such as spokes, etc, have negligible mass. The best approximation for $$\alpha ,$$ if the moment of inertia of the flywheel about its axis of rotation is expressed as $$\,\alpha M{R^2},\,\,$$ is ________.