A steel wire of length $4.7~\text m$ and cross-sectional area $3.0 \times 10^{-5}~\text{m}^2$ is stretched by the same amount as a copper wire of length $3.5~\text m$ and cross-sectional area of $4.0 \times 10^{-5}~\text m^2$ 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. $1.97:1$

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 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?
1. $4.86\times 10^{-6}~\text{m}$
2. $3.92\times 10^{-7}~\text{m}$
3. $3.01\times 10^{-7}~\text{m}$
4. $6.36\times 10^{-7}~\text{m}$

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 $1.03\times10^{3}~\text{kg m}^{-3}$?