Mechanical properties of solids practice · Medium

Equal torsional torques act on two rods $x\mathrm{ }and\mathrm{ }y$ having equal length. The diameter of rod $y$ is twice the diameter of rod $x.{\mkern 1mu} \,{\mkern 1mu} \mathrm{If}\,\,{\theta _x}{\mkern 1mu} {\mkern 1mu} \,and{\mkern 1mu} \,{\mkern 1mu} {\theta _y}$ are the angles of twist, then $\frac{{{\mathrm{\theta }_x}}}{{{\mathrm{\theta }_y}}} =$

The upper end of a wire of diameter $12 \mathrm{~mm}$ and length $1 \mathrm{~m}$ is clamped and its other end is twisted through an angle of $30^{\circ}$. The angle of shear is

The upper end of a wire of radius $\mathrm{4}\,\,\mathrm{mm}$ and length $\mathrm{100}\,\,\mathrm{cm}$ is clamped and its other end is twisted through and angle of ${30^0}$. Then angle of shear is

The bulk modulus of a spherical object is $'B'.$If it is subjected to uniform pressure $'p',$the fractional decreases in radius is

If a bar is made of copper whose coefficient of linear expansion is one and a half times that of iron, the ratio of the force developed in the copper bar to the iron bar of identical lengths and cross-sections, when heated through the same temperature range (Young’s modulus for copper may be taken equal to that of iron) is

A wire of length $\mathrm{L}$, area of cross section $\mathrm{A}$ is hanging from a fixed support. The length of the wire changes to ${\mathrm{L}_\mathrm{1}}$ when mass $\mathrm{M}$ is suspended from its free end. The expression for Young’s modulus is:

The general form of potential energy curve for atoms or molecules can be represented by the following equation $U\left( R \right) = \frac{A}{{{R^n}}} - \frac{B}{{{R^m}}}$ . Here, R is the interatomic or molecular distance, A and B are coefficients, $n$ and $m$ are the exponents. In the above equation

Which of the following relations is true

Find the density of the metal under a pressure of $20,000 \mathrm{~N} \mathrm{~cm}^{-2}$. Given density of the metal $=11 \mathrm{~g} \mathrm{~cm}^{-3}$, bulk modulus of the metal $=8 \times 10^9 \mathrm{~Nm}^{-2}$.

If the tension on a wire is removed at once, then:

A wire of length $4 \mathrm{~m}$ is hanged vertically from ceiling if it is stretched due to its own weight, then find out the energy stored per unit volume. $\left[Y=2 \times 10^7 \mathrm{~N} / \mathrm{m}^2\right.$ and $r=10^3$ $\mathrm{kg} / \mathrm{m}^3$ ]

When change in volume of a cube under a pressure at atm of 10 is 1% ; compressibility of material of black in ${m^2}/N$ is (Take 1atm $= {10^5}Pa$)

Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is $0.5\,\,cm$, the elongation $\left( l \right)$ of each wire is ${Y_s}\left( {\mathrm{steel}} \right) = 2.0 \times {10^{11}}N/{m^2}$, ${Y_c}\left( {\mathrm{copper}} \right) = 1.2 \times {10^{11}}N/{m^2}$

Assertion: If length of a rod is doubled, the breaking load remains the same.
Reason: Breaking load is equal to the elastic limit.

Young’s modulus of perfectly rigid body material is

A wire of Young’s modulus $1.5 \times {10^{12}}\;\mathrm{N}{\mathrm{m}^{ - 2}}$ is stretched by a force so as to produce a strain of $2 \times {10^4}.$ The energy stored per unit volume is

Which is the most elastic

If longitudinal strain for a wire is $\mathrm{0}\mathrm{.03}$ and its Poisson’s ratio is $\mathrm{0}\mathrm{.5}$, then its lateral strain is

If a spring extends by $x$ on loading, then the energy stored by the spring is (if $T$ is tension in the spring and $k$ is spring constant)

A $0.1$ kg mass is suspended from a wire of negligible mass. The length of the wire is $1\mathrm{ }m$ and its cross-sectional area is $4.9 \times {10^{ - 7}}{\mathrm{m}^{2.}}$ If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140\,\,\mathrm{rad}{\mathrm{s}^{ - 1}}$. If the Young’s modulus of the material of the wire is $n \times {10^9}\,\mathrm{N}{\mathrm{m}^{ - 2}}$, the value of $n$ is

What happens when the applied load increases and upto breaking stress in the experiment to determine the Young's modulus of elasticity?

A: Strain is a dimensionless quantity.
R: Strain is internal force per unit area of a body

In Searle's apparatus, used for study of extension of wires verses load, we have two wires. During the experiment, we study the extension in one wire. The use of second wire is

If ${G}=$ shear modulus and $Y=$ Young's modulus, then in general:

Statement I: With increase of temperature, elastic property of a substance decreases.
Statement II: Elasticity is due to intermolecular forces which decreases with the increase of inter molecular distance.

A 5 m long aluminium wire $Y = 7 \times {10^{10}}\;\mathrm{N}{\mathrm{m}^{ - 2\;}}$ of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in the copper wire $\left( {Y = 12 \times {{10}^2}\mathrm{Nm}{\mathrm{\;}^{ - 2}}} \right)\;$ of the same length under the same weight, the diameter should now be (in mm)

An elastic metal rod will change its length when it

A: It is the breaking stress and not the breaking strength which depends on the material
R: Breaking strength $=\frac{\text {Breaking stress}}{\text {Area}}$

A: Adiabatic elasticity of a gas is greater than isothermal elasticity
R: $\frac{E_{\text {adiabatic}}}{E_{\text {isothermal }}}=\gamma$

The breaking stress of a wire is $6 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ and density is $3 \times 10^3 \mathrm{Kg} / \mathrm{m}^3$. What should be the maximum length of the wire so that it may not break under its own weight?