What is the work done in stretching a uniform metal wire of length from 2 m to 2.004 m with an area of cross-section $10^{-6} \mathrm{~m}^2$ ?

[Young's modulus of the wire $=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ ]

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 $\times \pi \mathrm{kN}$. 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, $Y=2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )

Two wires of same length having radius of 2 mm and 1.5 mm respectively, are loaded with same weights. Extension of the second wire is double than that of the first wire. What is the ratio of the Young's modulus of the first wire to that of the second wire?

An object of mass 15 kg is attached to the end of a metal wire of unstretched length 1.0 m . The object is then whirled in a vertical circle with an angular velocity of $4 \mathrm{rad} / \mathrm{s}$ at the bottom of the circle. If the cross sectional area of the wire is $0.05 \mathrm{~cm}^2$ and Young's modulus of metal is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$, then the elongation of the wire when the mass is at the lowest point of its path (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )