Mechanical properties of solids practice · Mixed difficulty

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?

A rod elongated by $l$ when a body of mass $M$ is suspended from it. The work done is

A copper wire of negligible mass, $\mathrm{1 m}$ length and cross-sectional area ${10^{ - 6}}$ is kept on a smooth horizontal table with one end fixed. A ball of mass $\mathrm{1}$ kg is attached to the other end. The wire and the ball are rotated with an angular velocity 20 rad ${s^{ - 1}}$. If the elongation in the wire is ${10^{ - 3}}\mathrm{m}$, then the Young’s modulus is

The pressure on an object of bulk modulus B undergoing hydraulic compression due to a stress exerted by surrounding fluid having volume strain $\left(\frac{\Delta V}{V}\right)^2$ is

The maximum elongation of a steel wire of $1 \mathrm{~m}$ length if the elastic limit of steel and its Young's modulus, respectively, are $8 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2}$ and $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2},$ is:

Assertion: The force exerted by a spring is directly proportional to its displacement from its equilibrium position.

Reason: The spring force follows Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position.

Two rods of copper and steel having same area of cross - section but different lengths $l_{1}$ and $l_{2}$ respectively are connected to each other. The combined length of two rods fits between two walls without any stress on walls. If $\alpha_{1}$ and $\alpha_{2}$ are their coefficient of linear expansion, $Y_{1}$ and $Y_{2}$ are their Young's modulus respectively, then (There is no buckling of rods while heating) With increase in temperature:

Statement-I: If the volume of a body remains unchanged, When subjected to tensile strain, the value of Poisson's ratio is $1 / 2$
Statement-II: Phosphor bronze has low Young's modulus and high rigidity modulus

The approximate depth of an ocean is $3000 \mathrm{~m}$. The compressibility of water is $5 \times 10^{-10} \mathrm{~Pa}^{-1}$ and density of water is $10^3 \mathrm{~kg} / \mathrm{m}^3$. What fractional compression of water will be obtained at the bottom of the ocean.

A steel rod $y = 2 \times {10^{11}}\,N/{m^2}$ and $\alpha = {10^{ - 5}}/\,{\,^ \circ }C$ of length 1m and area of cross section $1\,c{m^2}$ is heated from ${0^ \circ }C$ to ${200^ \circ }C$ with out being allowed to extend or bend. What is the tension produced in the rod?

Energy stored in stretching a string per unit volume is

Stress to strain ratio is equivalent to

When a spiral spring is stretched by force, strain produced is

Two wires of same material and length but radii in the ratio 1 : 4 are stretched by two forces to produce equal elongation. The ratio of two forces is

Statement I: Glassy solids have sharp melting point.
Statement II: The bonds between the atoms of glassy solids broken at the same temperature.

The volume of a solid at 1 atmosphere pressure is $10^4 \mathrm{~cm}^3$. If the pressure is increased to 51 atmosphere then percentage change in its volume will be $\left(\mathrm{K}=10^{12}\right.$ dyne/ $\left.\mathrm{cm}^2\right)$-

In above question, the work done in the two wires is

Statement I: Stress is the internal force per unit area of the body.
Statement II: Rubber is more elastic than steel.

Assertion: A material which stretches more is more elastic.
Reason: Rubber is more elastic than steel.

The specific heat at constant pressure and at constant volume for an ideal gas are ${C_p}$ and ${C_v}$ and its adiabatic and isothermal elasticities are ${E_\phi }$ and ${E_\theta }$ respectively. The ratio of ${E_\phi }$ to ${E_\theta }$ is