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, 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 rectangular region in a solid is in a state of plane strain. The $$(x,y)$$ coordinates of the corners of the undeformed rectangle are given by $$P(0,0), Q(4,0), R(4,3), S(0,3).$$ The rectangle is subjected to uniform strains, $${\varepsilon _{xx}} = 0.001,\,\,{\varepsilon _{yy}} = 0.002,\,\,{\gamma _{xy}} = 0.003.$$ The deformed length of the elongated diagonal, upto three decimal places, is ______________ units.

Consider a beam with circular cross-section of diameter $$d.$$ The ratio of the second moment of area about the neutral axis to the section modulus of the area is