A cantilever beam having square cross-section of side $$a$$ is subjected to an end load. If a is increases by $$19$$%, the tip deflection decreases approximately by

A cantilever beam of length $$L$$ is subjected to a moment $$M$$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $$I$$ and the Young’s modulus is $$E$$. The magnitude of the maximum deflection is

A cantilever type gate hinged at $$Q$$ is shown in the figure. $$P$$ and $$R$$ are the centers of gravity of the cantilever part and the counterweight respectively. The mass of the cantilever part is $$75$$ kg. The mass of the counterweight, for static balance, is

Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the load P is applied, the free ends will have