Every material obeys Hooke’s law within its

Important Questions on Mechanical Properties of Solids

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

The elastic limit of brass is $379\mathrm{ }\mathrm{M}\mathrm{P}\mathrm{a}$. The minimum diameter of a brass rod if it is to support a $400\mathrm{ }\mathrm{N}$ load without exceeding its elastic limit will be

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

A steel wire having a radius of $2.0 \mathrm{m}\mathrm{m}$ , carrying a load of $4 \mathrm{k}\mathrm{g},$ is hanging from a ceiling. Given that $\mathrm{g}=3.1\mathrm{\pi }\mathrm{ }\mathrm{m }{\mathrm{s}}^{-2},$ what will be the tensile stress that would be developed in the wire?

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

For a perfectly rigid body,

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

An object of mass $\mathrm{m}$ is suspended at the end of a massless wire of length $\mathrm{L}$ and area of cross-section, A. Young modulus of the material of the wire is $Y$. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

The value of $\tan \theta$ in the graph gives

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

A cube of metal is subjected to a hydrostatic pressure $4 \mathrm{GPa}$. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, $B=8\times {10}^{10} \mathrm{Pa}$)

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

Copper of fixed volume $V$ is drawn into wire of length $l$. When this wire is subjected to a constant force $F,$ the extension produced in the wire is $∆l.$ Which of the following graph is a straight line?

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

The wrong statement in the following is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

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:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

In materials like aluminium and copper,  the correct order of magnitude of various elastic modulii is :

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

A wire of length $L$, area of cross section $A$ is hanging from a fixed support. The length of the wire changes to $L_1$ when mass $M$ is suspended from its free end. The expression for Young’s modulus is:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

A wire of diameter $1 \mathrm{mm}$ breaks under a tension of $1000 \mathrm{N}$. Another wire of the same material as that of the first one, but of diameter $2 \mathrm{mm}$ breaks under a tension of:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

$A$ and $B$ are two wires. The radius of $A$ is twice that of $B$. They are stretched by the same load. Then the stress on $B$ is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

A metallic rod breaks when strain produced is $0.2\%$. Young's modulus of the material of the rod is $7\times {10}^9 \mathrm{N} {\mathrm{m}}^{-2}$. What should be its area of cross-section to support a load of ${10}^4 \mathrm{N}$?

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

The Young's modulus of a perfectly rigid body is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

Consider a metallic wire of length $10 \mathrm{m}$. An external force applied results in an elongation of $5 \mathrm{mm}$. What is the potential energy stored per unit volume
[Young's modulus of wire $Y=16\times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2}$]

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

The speed of the water in a river is $V$ near the surface. If the coefficient of viscosity of water is $\eta$ and the depth of the river is $H$, then the shearing stress between the horizontal layers of water is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

When a block of mass $M$ is suspended by a long wire of length $L$, the length of the wire becomes $\left(L+l\right).$ The elastic potential energy stored in the extended wire is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A.$ If the length of the first wire is increased by $∆l$ on applying a force $F,$ how much force is needed to stretch the second wire by the same amount?

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Stress and Strain Curve

Breaking stress of a steel wire is $p$ and the density of steel is $\rho$. The greatest length of steel wire that can hang vertically without breaking is