$A$ steel rod with a circular cross-section of diameter $1 \ cm$ and another steel rod with a square cross-section of side $1 \ cm$ have equal mass. If the two rods are subjected to the same tension, the ratio of the elongations of the two rods is

$A$ structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. $A$ $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress,$(b)$ elongation,and $(c)$ strain on the rod. Young's modulus of structural steel is $2.0 \times 10^{11} \;N \;m^{-2}$.

One end of a steel rod of radius $10.0 \ mm$ and length $50.0 \ cm$ is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude $10.0 \times \pi \ kN$. This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (Use Young's modulus $= 2.0 \times 10^{11} \ N/m^2$) (in $mm$)

$A$ bar is subjected to axial forces as shown. If $E$ is the modulus of elasticity of the bar and $A$ is its cross-section area,its total elongation will be:

$A$ steel rod of radius $20 \ mm$ and length $2 \ m$ is acted upon by a force of $400 \ kN$ along its length. The values of stress and strain are respectively $(Y_{\text{steel}} = 2 \times 10^{11} \ N \ m^{-2})$.

Two metallic wires $P$ and $Q$ have the same volume and are made up of the same material. If their areas of cross-section are in the ratio $4:1$ and a force $F_1$ is applied to $P$,an extension of $\Delta l$ is produced. The force required to produce the same extension in $Q$ is $F_2$. The value of $\frac{F_1}{F_2}$ is . . . . . . .