The bulk modulus for an incompressible liquid is .

Important Questions on Mechanical Properties of Solids

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

Young's moduli of two wires $\mathrm{A}$ and $\mathrm{B}$ are in the ratio $7:4$ . Wire $\mathrm{A}$ is $2 \mathrm{m}$ long and has radius $\mathrm{R}.$ Wire $\mathrm{B}$ is $1.5 \mathrm{m}$ long and has radius $2\mathrm{ }\mathrm{m}\mathrm{m}.$ If the two wires stretch by the same length for a given load, the value of $\mathrm{R}$ is close to:

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A uniformly tapering conical wire is made from a material of Young's modulus $Y$ and has a normal, unextended length $L$. The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R$, respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal:

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A thin $1 \mathrm{m}$ long rod has a radius of $5 \mathrm{mm}$. A force of $50{\text{π×10}}^3 \mathrm{N}$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01 \mathrm{mm}$, which of the following statements is false?

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A wire is stretched such that its volume remains constant. The Poisson’s ratio of the material of the wire is:

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

An external pressure $P$ is applied on a cube at $0°\mathrm{C}$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

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?

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A bottle has an opening of radius $\mathrm{a}$ and length $\mathrm{b}$. A cork of length $\mathrm{b}$ and radius $\left(\mathrm{a}+∆\mathrm{a}\right)$ where $\left(∆\mathrm{a}\ll \mathrm{a}\right)$, is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is $\mathrm{B}$ and the coefficient of friction between the bottle and cork is $\mathrm{\mu }$, then the force needed to push the cork into the bottle is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

The Young's modulus of a perfectly rigid body is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A steel rail of length $5 \mathrm{m}$ and area of cross section $40 {\mathrm{cm}}^2$ is prevented from expanding along its length while the temperature rises by $10°\mathrm{C}$ . If coefficient of linear expansion and Young's modulus of steel are $1.2\times {10}^{-5} {\mathrm{K}}^{-1}$ and $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ respectively, the force developed in the rail is approximately:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

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

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

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 :

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to $T_M$ . If the Young's modulus of the material of the wire is $Y$, then $\frac{1}{Y}$ is equal to:
($g=$gravitational acceleration)

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

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:

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A steel wire of diameter $0.5 \mathrm{mm}$ and Young's modulus $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ carries a load of mass $M$. The length of the wire with the load is $1.0 \mathrm{m}$. A vernier scale with $10$ divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count $1.0 \mathrm{mm}$, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by $1.2 \mathrm{kg}$, the vernier scale division which coincides with a main scale division is __________. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2} \text{and} \mathrm{\pi }= 3.2$.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A cubical solid aluminum $\left(\mathrm{bulk} \mathrm{modulus}=-V\frac{\mathrm{d}P}{\mathrm{d}V}=70 \mathrm{GPa}\right)$ block has an edge length of $1 \mathrm{m}$ on the surface of the earth. It is kept on the floor of a $5 \mathrm{km}$ deep ocean. Taking the average density of water and the acceleration due to gravity to be ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and $10 \mathrm{m} {\mathrm{s}}^{-2}$, respectively, the change in the edge length of the block in $\mathrm{mm}$ is ________.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

What is the pressure required to reduce the given volume of water by $1\%$ ? (Bulk modulus $\left(K\right)=2\times {10}^8 \mathrm{N} {\mathrm{m}}^{-2}$)

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A rubber cord has a cross-sectional area ${10}^{-6} {\mathrm{m}}^2$ and total unstretched length $0.1 \mathrm{m}$. It is stretched to $0.125 \mathrm{m}$ and then released to project a particle of mass $5.0 \mathrm{g}$. The velocity of projection is [Given, Young's modulus of rubber, $Y=5\times {10}^8 \mathrm{N} {\mathrm{m}}^{-2}$]

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area $a$ floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere $\left(\frac{dr}{r}\right)$ , is:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Moduli

A load of mass $M \mathrm{kg}$ is suspended from a steel wire of length $2 \mathrm{m}$ and radius $1.0 \mathrm{mm}$ in Searle's apparatus experiment. The increase in length produced in the wire is $4.0 \mathrm{mm}.$ Now the load is fully immersed in a liquid of relative density $2.$ The relative density of the material of load is $8.$ The new value of increase in length of the steel wire is: