If the ratio of diameters,lengths and Young's moduli of steel and brass wires shown in the figure are $p, q$ and $r$ respectively,then the corresponding ratio of increase in their lengths would be

Two wires of copper having the lengths in the ratio $4:1$ and their radii in the ratio $1:4$ are stretched by the same force. The ratio of longitudinal strain in the two will be

$A$ rod of length $l$ and area of cross-section $A$ is heated from $0^{\circ}C$ to $100^{\circ}C$. The rod is so placed that it is not allowed to increase in length,then the force developed is proportional to

With a rise in temperature,the Young's modulus of elasticity

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} \; \text{kg}$. The inner and outer radii of each column are $50 \; \text{cm}$ and $100 \; \text{cm}$ respectively. Assuming uniform load distribution,calculate the compressive strain of each column. [Use $Y = 2.0 \times 10^{11} \; \text{Pa}$,$g = 9.8 \; \text{m/s}^2$]

The length of a wire is $l_1$ when a mass $M_1$ is hung from it,and it is $l_2$ when both masses $M_1$ and $M_2$ are hung from it. The natural length of the wire is ........