A point $$P\left( {1,\,\,\,3,\,\,\, - 5} \right)$$ is translated by $$2\widehat i + 3\widehat j - 4\widehat k$$ and then rotated counter clockwise by $${90^ \circ }$$ about the $$z$$-axis. The new position of the point is

A square plate of dimension L $$ \times $$ L is subjected to a uniform pressure load P = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus E = 200 GPa.

The deformed shape is a square of dimension 𝐿 − 2$$\delta .$$ If 𝐿 = 2 m and $$\delta $$ = 0.001 m, the Poisson’s ratio of the plate material is __________ .

The state of stress at a point on an element is shown in figure (a). The same state of stress is shownin another coordinate system in figure (b).

The components $$\left( {{\tau _{xx,}}{\tau _{yy,}}{\tau _{xy}}} \right)$$ are given by

The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity $${{\rm I}_1}$$ while the circular cross-section has flexural rigidity $${{\rm I}_2}$$. Both sections have the same cross-sectional area. The ratio $${{\rm I}_1}$$/$${{\rm I}_2}$$ is