The dimensional formula of Young's modulus is: 

Important Questions on Mechanics of Solids and Fluids

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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, $B=8\times {10}^{10} \mathrm{Pa}$)

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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:

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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?

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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 :

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-strain Curve

A metal rod of cross-sectional area $3\times {10}^{-6} {\mathrm{m}}^2$ is suspended vertically from one end has a length $0.4 \mathrm{m}$ at $100 °\mathrm{C}$. Now the rod is cooled upto $0 °\mathrm{C}$, but prevented from contracting by attaching a mass $m$ at the lower end. The value of $m$ is ($Y={10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$, coefficient of linear expansion $={10}^{-5} {\mathrm{K}}^{-1}, g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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?

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-strain Curve

For a perfectly rigid body,

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-strain Curve

The wrong statement in the following is

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-strain Curve

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

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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 $Y=16\times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2}$]

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-strain Curve

The Young's modulus of a perfectly rigid body is

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-strain Curve

A bar is made up of material whose Young's modulus is $E$, Poisson's ratio $\mu$ and is subjected to hydrostatic pressure $p$. The fractional change in its volume $\left(\frac{\mathrm{\Delta }V}{V}\right)$ is

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-strain Curve

If $S$ is the stress and$Y$ is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-strain Curve

A rubber cube of side $5 \mathrm{cm}$ has one face fixed while a tangential force $1800 \mathrm{N}$ is applied on its opposite face. If modulus of rigidity of rubber is $2.4\times {10}^6 \mathrm{N} {\mathrm{m}}^{-2}$, then the lateral displacement of the strained face is______.

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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 ${10}^4 \mathrm{N}$?

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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

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General Science>Physics>Mechanics of Solids and Fluids>Hooke's Law and Stress-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: