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:

The figure shows the stress-strain curve for a given material. The approximate yield strength for this material is:
         
1. \(3\times10^8~\text{N/m}^2\)
2. \(2\times10^8~\text{N/m}^2\)
3. \(4\times10^8~\text{N/m}^2\)
4. \(1\times10^8~\text{N/m}^2\)

The stress-strain graphs for materials \(A\) and \(B\) are shown in the figure. Young’s modulus of material \(A\) is:
(the graphs are drawn to the same scale)

The stress-strain graphs for materials \(A\) and \(B\) are shown in the figure. The strength of the material \(A\) is:
(The graphs are drawn to the same scale)
       

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)

The edge of an aluminum cube is \(10~\text{cm}\) long. One face of the cube is firmly fixed to a vertical wall. A mass of \(100~\text{kg}\)  is then attached to the opposite face of the cube. The shear modulus of aluminum is \(25~\text{GPa}.\) What is the vertical deflection of this face?

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, \(Y = 2\times 10^{11}~\text{Pa}\)$$)

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 \(0.065~\text{cm}^2\). The elongation of the wire when the mass is at the lowest point of its path is:
(Young's modulus = \(2×10^{11}~\text{N/m}^2\))

What is the density of water at a depth where pressure is \(80.0\) atm, given that its density at the surface is \(1.03\times10^{3}~\text{kg m}^{-3}\)?