Ignoring the small elastic region, the true stress (𝜎) – true strain (𝜀) variation of a material beyond yielding follows the equation 𝜎 = 400𝜀^0.3 MPa. The engineering ultimate tensile strength value of this material is ________ MPa.

(Rounded off to one decimal place)

A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm². Its elastic modulus varies along its length as given by E(x) = 100 e^-x GPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.

A point mass of $$100$$ kg is dropped onto a massless elastic bar (cross-sectional area = $$100$$ $$mm$$² ,length = $$1$$ m, Young's modulus = $$100$$ GPa) from a height $$H$$ of $$10$$ $$mm$$ as shown (Figure is not to scale). If g = $$10$$ $$m/s$$² , the maximum compression of the elastic bar is _______ $$mm.$$

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 ________.