Elasticity

A student performs an experiment to determine the Young’s modulus of a wire, exactly $2 \mathrm{m}$ long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \mathrm{mm}$ with an uncertainty of $\pm 0.05 \mathrm{mm}$ at a load of exactly $1.0 \mathrm{kg}$. The student also measures the diameter of the wire to be $0.4 \mathrm{mm}$ with an uncertainty of $\pm 0.01 \mathrm{mm}$. Take $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$ (exact). The Young’s modulus obtained from the reading is

A wire of length $2 \mathrm{m}$is made from $10 {\mathrm{cm}}^3$of copper. A force$F$ is applied so that its length increase by $2 \mathrm{mm}$. Another wire of length$8 \mathrm{m}$ is made from the same volume of copper. If the force $F$is applied to it, its length will increase by

A rod of iron of Young's modulus $Y=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ just fits the gap between two rigid supports $1 \mathrm{m}$ apart. If the rod is heated through$100 °\mathrm{C}$the strain energy of the rod is ($a=18\times {10}^{-6} {\mathrm{m}}^2$ area of cross-section)

A steel rod of length $1 \mathrm{m}$ and cross-sectional area ${10}^{-4} {\mathrm{m}}^2$ is heated from $0°\mathrm{C}$ to $200°\mathrm{C}$ without being allowed to extend or bend. The compressive tension produced in the rod is _____$\times {10}^4 \mathrm{N}$. (Given Young's modulus of steel $=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$, coefficient of linear expansion $={10}^{-5} {\mathrm{K}}^{-1}$ )

The length of a wire becomes $l_1$ and $l_2$ when $100 \mathrm{N}$ and $120 \mathrm{N}$ tension are applied respectively. If $10l_2=11l_1$, then the natural length of wire will be $\frac{1}{x}{l}_1$. Here the value of $x$ is

The elastic potential energy stored in a steel wire of length $20 \mathrm{m}$ stretched through $2 \mathrm{cm}$ is $80 \mathrm{J}.$ The cross sectional area of the wire is _____ ${\mathrm{mm}}^2.$ (Given, $Y=2.0\times {10}^{11} \mathrm{N} {\mathrm{m}}^{–2}$)

Under isothermal condition, the pressure of a gas is given by $P=a{V}^{–3},$ where $a$ is a constant and $V$ is the volume of the gas. The bulk modulus at constant temperature is equal to

A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force$f$, its length increases by $l$. Another wire of same material of length $2L$ and radius $2r$ is pulled by a force $2f$. Then the increase in its length will be:

Two wires each of radius $0.2 \mathrm{cm}$ and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is ______${10}^{–6} \mathrm{m}$. [Young's modulus for steel $=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{–2}$ and $g=10 \mathrm{m} {\mathrm{s}}^{–2}$]

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

An aluminium rod with Young’s modulus $\mathrm{Y}=7.0 \times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2}$ undergoes elastic strain of $0.04\%$. The energy per unit volume stored in the rod in $\mathrm{SI}$ unit

A metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter $14 \mathrm{mm}$. The tensile stress developed in the wire under equilibrium state is $7\times {10}^5 \mathrm{N} {\mathrm{m}}^{–2}$. The value of mass $m$ is ______ $\mathrm{kg}$.

(Take $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$ and $\pi =\frac{22}{7}$)

A hydraulic automobile lift is designed to lift vehicles of mass $5000 \mathrm{kg}$. The area of cross section of the cylinder carrying load is $250 {\mathrm{cm}}^2$. The maximum pressure the smaller piston would have to bear is [Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$]

Young’s moduli of the material of wires A and B are in the ratio of $1 : 4$, while its area of cross sections are in the ratio of $1 : 3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [Assume length of wires A and B are same]

Pressure for polytropic process $P$ varies with volume $V$ as $P=a{V}^{-3}$, Find out the bulk modulus.

A material has Poisson's ratio $0.5_{}$ and Young's modulus$2\times {10}^{11} \mathrm{Pa}$. If a uniform rod of it suffers a lateral strain of$4\times {10}^{-6}$, then percentage change in its density will be

Wires $A$ and $B$ have their Young's moduli in the ratio $1:3$, area of cross-section in the ratio of $1:2$ and lengths in ratio of $3:4$. If same force is applied on the two wires to elongate, then ratio of elongation is equal to

 A cast iron column has internal diameter of $200 \mathrm{mm}$. What should be the minimum external diameter so that it may carry a load of $1.6 \mathrm{MN}$ without the stress exceeding $90 \mathrm{N} {\mathrm{mm}}^2$

Assertion(A): Steel is used to build big structures.

Reason(R): Steel has more elastic modulus as compared to other materials.

If the length of a wire is made double and radius is halved of its respective values. Then, the Young’s modulus of the material of the wire is