A metallic rod of cross-sectional area $A$ is subjected to equal and opposite tensile forces $F$ at its ends as shown in figure. Consider a plane $x{x}^{\text{'}}$ making an angle $\theta$ as indicated in figure. For what value of $\theta$ is the shearing stress on plane $x{x}^{\text{'}}$ is maximum?

A uniform rod of length $2L$, area of cross-section $A$ and Young's modulus $Y$ is lying at rest under the action of three forces as shown.

Select the correct alternatives.

Two thin wires $A$ and $B$ of equal length $L$ and equal cross-sectional area $A$ and masses $M_1$ and $M_2$ respectively are joined end to end and suspended as shown in the figure. Wires $A$ and $B$ have Young's modulus $Y_1$ and $Y_2$ respectively. The total elongation in the combined wire is