Two wires $A$ and $B$ are made of the same material. Their diameters are in the ratio of $1: 2$ and their lengths are in the ratio of $1: 3$. If they are stretched by the same force,then the increase in their lengths will be in the ratio of:

$A$ wire extends by $1 \ mm$ when a force is applied. If double the force is applied to another wire of the same material and length but half the radius of the cross-section,what will be the elongation of the wire in $mm$?

The diameter of a brass rod is $4 \ mm$ and Young's modulus of brass is $9 \times 10^{10} \ N/m^2$. The force required to stretch it by $0.1\%$ of its original length is:

Two wires $A$ and $B$ of the same cross-section are connected end to end. When the same tension is applied to both wires,the elongation in wire $B$ is twice the elongation in wire $A$. If $L_A$ and $L_B$ are the initial lengths of the wires $A$ and $B$ respectively,then (Young's modulus of material of wire $A = 2 \times 10^{11} \ Nm^{-2}$ and Young's modulus of material of wire $B = 1.1 \times 10^{11} \ Nm^{-2}$):

$A$ metallic bar of Young's modulus $0.5 \times 10^{11} \,N \,m^{-2}$, coefficient of linear thermal expansion $10^{-5} \,^{\circ}C^{-1}$, length $1 \,m$, and area of cross-section $10^{-3} \,m^2$ is heated from $0^{\circ}C$ to $100^{\circ}C$ without expansion or bending. The compressive force developed in it is:

The value of Young's modulus for a perfectly rigid body is ...........