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A circular wire of radius $R$, placed on a horizontal surface is made to rotate about a fixed vertical axis passing through its center as shown. If breaking stress of the material of wire is $S_0$, then find maximum value of $\omega$ so that wire does not break (Cross-sectional area of wire is $A,\lambda$ is the linear mass density of wire)

Consider an arrangement shown in the diagram which is combination of two rods (1) and (2). Their length, cross-sectional area and Young's modulus are shown in diagram. If force $F_0$ is applied at end $Q$ of rod (2), then total elongation of combined system is $[$ $P$ is the common end of rod (1) and (2)$]$

Consider a metal rod shown in figure. Two forces are applied at the ends of the rod. Find displacement of point $P$

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?