Elastic Behaviour, Stress & Strain

The strain-stress plot for materials $A, B, C$ and $D$ is shown in the figure. Which material has the largest Young's modulus?

A uniform wire of length $l$ of weight $w$ is suspended from the roof with a weight of $W$ at the other end. The stress in the wire at $\frac{l}{3}$ distance from the top is $\left(\frac{W}{A} + \frac{2}{\gamma}\frac{w}{A}\right)$, where $A$ is the cross sectional area of the wire. The value of $\gamma$ is ________.

With rise in temperature, the Young's modulus of elasticity:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.

Reason (R): The restoring force depends upon the bonded inter atomic and inter molecular force of solid.

In the light of the above statements, choose the correct answer from the options given below:

Match List I with List II:

Choose the correct answer from the options given below:

One end of a metal wire is fixed to a ceiling and a load of $2\text{ kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1\text{ kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ________. [Area of cross section of wire $= 0.005\text{ cm}^2, Y = 2 \times 10^{11}\text{ N m}^{-2}$ and $g = 10\text{ m s}^{-2}$ ]

Two blocks of mass $2\text{ kg}$ and $4\text{ kg}$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0 \times 10^{-5}\text{ m}$ and Young's modulus of the metal is $2.0 \times 10^{11}\text{ N/m}^2$. The longitudinal strain developed in the wire is $\frac{1}{\alpha\pi}$. The value of $\alpha$ is _________. [Use $g = 10\text{ m/s}^2$]

Each of three blocks $P, Q$ and$R$ shown in figure has a mass of $3\text{ kg}$. Each of the wires $A$ and $B$ has cross-sectional area $0.005\text{ cm}^2$ and Young's modulus $2 \times 10^{11}\text{ N m}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is ________ $\times 10^{-4}$. (Take $g = 10\text{ m/s}^2$)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Steel is used in the construction of buildings and bridges.

Reason R: Steel is more elastic and its elastic limit is high.

In the light of above statements, choose the most appropriate answer from the options given below

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of cross-sectional area $A$ of the wire is:

A metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter $14\text{ mm}$. The tensile stress developed in the wire under equilibrium state is $7 \times 10^{5}\text{ N m}^{-2}$. The value of mass $m$ is _________ $\text{kg}$. (Take, $g = 9.8\text{ m s}^{-2}$ and $\pi = \frac{22}{7}$)

A steel rod has a radius of $20\text{ mm}$ and a length of $2.0\text{ m}$. A force of $62.8\text{ kN}$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\text{ N/m}^2$. The longitudinal strain produced in the wire is _____________ $\times 10^{-5}$

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring.

Reason (R): A coil spring of copper has more tensile strength than a steel spring of same dimensions.

In the light of the above statements, choose the most appropriate answer from the options given below:

A block of mass M is attached to a wire. The upper part of wire is made of steel and lower part of wire of copper ( as shown in figure ). Both parts have the same area of cross section. Neglecting the mass of wires, the ratio of longitudinal strain developed in steel and copper wires is: ( Given, Young's modulus of steel $= 2 \times 10^{11}\text{ N/m}^2$ and Young's modulus of copper $= 1.5 \times 10^{11}\text{ N/m}^2$)

A string of area of cross-section $4\text{ mm}^2$ and length $0.5\text{ m}$ is connected with a rigid body of mass $2\text{ kg}$. The body is rotated in a vertical circular path of radius $0.5\text{ m}$. The body acquires a speed of $5\text{ m/s}$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _________ $\times 10^{-5}$.

(use Young's modulus $10^{11}\text{ N/m}^2$ and $g = 10\text{ m/s}^2$)

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $\times$ 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $\times$ 1011 Pa, g = 9.8 m/s2]

Two wires $A$ and $B$ are stretched by the same load. The radius of wire $A$ is double the radius of wire $B$. The stress on the wire $B$ as compared to the stress on the wire $A$ is

Two wires of different materials have same length $L$ and same diameter $d$. The second wire is connected at the end of the first wire and forms one single wire of double the length. This wire is subjected to stretching force $F$ to produce the elongation I. The two wires have

Two identical wires of substances ' $P$ ' and ' $Q$ ' are subjected to equal stretching force along the length. If the elongation of ' $Q$ ' is more than that of ' $P$ ', then

A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1$\pi$ ms–2, what will be the tensile stress that would be developed in the wire?

The stress-strain curves are drawn for two different materials X and Y. It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y.

We can say that materials X and Y are likely to be (respectively),

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of: