Mechanical properties of solids practice · Mixed difficulty

Two steel wires have equal volumes, their diameters are in the ratio $2:1$. When same force is applied on them, the elongation produced will be in the ratio of

Breaking stress of a steel wire of radius $1 \mathrm{~mm}$ and length $1 \mathrm{~m}$ is $10^{12} \mathrm{~N} / \mathrm{m}^2$. Breaking stress of another steel wire of radius $2 \mathrm{~mm}$ and length $0.5 \mathrm{~m}$ will be

The ratio of two specific heats of gas ${C_p}/{C_v}$ for argon is $\mathrm{1}\mathrm{.6}$ and for hydrogen is $\mathrm{1}\mathrm{.4}$. Adiabatic elasticity of argon at pressure $P$ is $E$. Adiabatic elasticity of hydrogen will also be equal to $E$ at the pressure

A: When a beam is bent only tensile strain is produced.
R: The depression produced in a rectangular beam is directly proportional to its width.

Under elastic limit the stress is

A copper bar of length $L$ and area of cross-section $A$ is placed in a chamber at atmospheric pressure. If the chamber is evacuated, the percentage change in its volume will be (compressibility of copper is $8\,\, \times \,{10^{12}}\,\mathrm{m}{\,^2}{\mathrm{N}^{ - 1}}\mathrm{and}\,\,1\,\,\mathrm{atm} = {10^5}\,\,\mathrm{N}{\mathrm{m}^2})$

What is the nature of intermolecular forces?

$K$ is the force constant of a spring. The work done in increasing its extension from ${l_1}$ to ${l_2}$ will be

The value of Poisson’s ratio lies between

Assertion: The stretching of a coil is determined by its Shear modulus.
Reason: Shear modulus changes only shape of a body keeping its dimensions unchanged.

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 ${Y_s}\left( {\mathrm{steel}} \right) = 2.0 \times {10^{11}}N/{m^2}$, ${Y_c}\left( {\mathrm{copper}} \right) = 1.2 \times {10^{11}}N/{m^2}$

A long piece of rubber is wider than it is thick. When is is stretched in length by some amount:

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)