A heavy rope is suspended from the ceiling of a room. If $\rho$ is the density of the rope, $L$ be its original length and $Y$ be its Young's modulus, then increase $\Delta L$ in the length of the rope due to its own weight is

What is the greatest length of copper wire that can hang without breaking?

Breaking stress $=7.2\times {10}^7 \mathrm{N} {\mathrm{m}}^{–2},$ Density of copper $=7.2 \mathrm{g} {\mathrm{cc}}^{–1}, g=10 \mathrm{m} {\mathrm{s}}^{–2}$

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)$]$