A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s modules for the sections AB and BC are 3E and E, respectively.
For the deflection at C to be zero, the ratio P/F is ________.

The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in mm⁴) of this cross-section about its base is __________.

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

The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that 𝑟₃ > 𝑟₁ and 𝑟₄ > 𝑟₂ , and that the areas of the cross-sections are the same. J₁ and J₂ are the torsional rigidities of the bars on the left and right, respectively. The ratioJ₂/J₁ is