A block of mass 2 kg is tied to one end of a 2 m long metal wire of $1.0 \mathrm{~mm}^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is 2 mm , the Young's modulus of the metal is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If the length of a string is $P$ when the tension in it is 6 N and its length is $Q$ when the original length of the string is

A steel wire of length 3 m and a copper wire of length 2.2 m are connected end to end. When the combination is stretched by a force, the net elongation is 1.05 mm . If the area of cross-section of each wire is $6 \mathrm{~mm}^2$, then the load applied is (Young's moduli of steel and copper are respectively $2 \times 10^{11} \mathrm{Nm}^{-2}$ and $1.1 \times 10^{11} \mathrm{Nm}^{-2}$ )

The ratio of the areas of cross-sections of three wires is $1: 2: 3$ and the ratio of the Young's modulii of their materials is $3: 2: 1$. If the three wires are of same length and same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is