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):

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 aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 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, $\mathrm{Y}=2\times {10}^{11} \mathrm{Pa}$)$$

A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 10⁸ N/m², what is the maximum load that the cable can support?

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:

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×${10}^3$ $\mathrm{kg} {\mathrm{m}}^{-3}$?

The volume contraction of a solid copper cube, 10 cm on an edge, when
subjected to a hydraulic pressure of 7.0×${10}^6 \mathrm{Pa}$ is:

(Bulk modulus of copper is $140\times {10}^9 \mathrm{Pa}$.)

How much should the pressure on a litre of water be changed to compress it by 0.10%?

(Given Bulk modulus of water, $\mathrm{B}=2.2\times {10}^9 {\mathrm{Nm}}^{-2}$)

$$\begin{gathered} \left(1\right) 4.8\times {10}^6 \mathrm{N}/{\mathrm{m}}^2 \\ \left(2\right) 2.2\times {10}^6 \mathrm{N}/{\mathrm{m}}^2 \\ \left(3\right) 5.1\times {10}^6 \mathrm{N}/{\mathrm{m}}^2 \\ \left(4\right) 3.3\times {10}^6 \mathrm{N}/{\mathrm{m}}^2 \end{gathered}$$

Anvils made of single crystals of diamond, with the shape as shown in the figure, are used to investigate the behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.50 mm, and the wide ends are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil?

A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in the figure. The cross-sectional areas of wires A and B are 1.0 $m{m}^2$ and 2.0 $m{m}^2$, respectively. At what point along the rod should a mass m be suspended in order to produce equal stresses in both steel and aluminium wires?
           

Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9×${10}^7$ Pa? (Assume that each rivet is to carry one-quarter of the load.)

The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of the water. The water pressure at the bottom of the trench is about 1.1 ×${10}^8$ Pa. A steel ball of initial volume 0.32 $m^3$ is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom? [Given:$B_{steel}=1.6\times {10}^{11} N m^{-2}$]

$$\begin{gathered} \left(1\right) 1.01\times {10}^{-3} {\mathrm{m}}^3 \\ \left(2\right) 2.2\times {10}^{-4} {\mathrm{m}}^3 \\ \left(3\right) 1.9\times {10}^{-3} {\mathrm{m}}^3 \\ \left(4\right) \mathrm{None} \mathrm{of} \mathrm{these}. \end{gathered}$$

Select the correct alternative(s).

Which of the following affects the elasticity of a substance?

Select the wrong definition.

The shear strain is possible in

The ratio of radii of two wires of the same material is 2: 1. If these wires are stretched by equal force, the ratio of stresses produced in them is:

A steel wire of diameter 2 mm has a breaking strength of $4\times {10}^5 \mathrm{N}$. What is the breaking force of similar steel wire of diameter 1.5 mm?

A steel wire is 1 m long and 1 mm² in area of cross section. If it takes 200 N to stretch this wire by 1 mm, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of 10 m to a length of 1002 cm?

What is the percentage increase in length of a wire of diameter 2.5 mm, stretched by a force of 100 kg wt? Young's modulus of elasticity of wire$=12.5\times {10}^{11} \mathrm{dyne}/{\mathrm{cm}}^2$

A rod of length l and radius r is held between two rigid walls so that it is not allowed to expand. If its temperature is increased, then the force developed in it is proportional to

A uniform cubical block is subjected to volumetric compression, which decreases its each side by 2%. The Bulk strain produced in it is

A material has Poisson's ratio 0.5. If a uniform rod of it suffers a longitudinal strain of $3\times {10}^{-3}$, what will be percentage increase in volume?

Hooke's law is applicable for:

When a load of 10 kg is suspended on a metallic wire, its length increase by 2mm. The force constant of the wire is

The figure shows the graph between stress and strain for a uniform wire at two different temperatures. Then:

If two different types of rubber are found to have stress-strain curves as shown, then:
                   

The stress-strain graphs for two materials A and B are shown in the figure. The graphs are drawn to the same scale. Select the correct statement:

The load versus elongation graph for four wires of same length and the same material is shown in figure. The thinnest wire is represented by line: