A steel wire of length \(4.7\) m and cross-sectional area \(3.0 \times 10^{-5}\) m² is stretched by the same amount as a copper wire of length \(3.5\) m and cross-sectional area of \(4.0 \times 10^{-5}\) m² under a given load. The ratio of Young’s modulus of steel to that of copper is:
1. \(1.79:1\)
2. \(1:1.79\)
3. \(1:1\)
4. \(1.97:1\)

Two wires of diameter \(0.25\) cm, one made of steel and the other made of brass are loaded, as shown in the figure. The unloaded length of the steel wire is \(1.5\) m and that of the brass wire is \(1.0\) m. The elongation of the steel wire will be:
(Given that Young's modulus of the steel, \(Y_S=2 \times 10^{11}\) Pa$\mathrm{}$ and Young's modulus of brass, \(Y_B=1 \times 10^{11}\) Pa)

Four identical hollow cylindrical columns of mild steel support a big structure of a mass of 50,000 kg. The inner and outer radii of each column are 30 cm and 60 cm respectively. Assuming the load distribution to be uniform, the compressional strain of each column is: (Given, Young's modulus of steel, $\mathrm{Y}=2\times {10}^{11}$ $\mathrm{Pa}$)$$
1. 3.03×10^-7

2. 2.8×10^-6

3. 7.22×10^-7

4. 4.34×10^-7

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 ${\mathrm{cm}}^2$. The elongation of the wire when the mass is at the lowest point of its path is:(Young's modulus = 2*10¹¹N/m²)

$1. 7.01\times {10}^{-3} m$

$$
$2. 2.35\times {10}^{-3} m$

$$
$3. 1.87\times {10}^{-3} m$

$$
$4. 3.31\times {10}^{-3} m$