Distinguish between elasticity and plasticity.

Important Questions on Mechanical Properties of Solids

HARD

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

In plotting stress versus strain curves for two materials $P$ and $Q$ , a student by mistake puts strain on the $y$ -axis and stress on the $x$ - axis as shown in the figure. Then the correct statement(s) is(are)

HARD

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

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:

MEDIUM

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

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:

EASY

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

One end of a horizontal thick copper wire of length $2\mathrm{L}$and radius $2\mathrm{R}$ is welded to an end of another horizontal thin copper wire of length$\mathrm{L}$ and radius$\mathrm{R}$. When the arrangement stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is 

MEDIUM

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

A particle of mass $1 \mathrm{kg}$ is moving in SHM with a path length of $0.01 \mathrm{m}$ and frequency of $50 \mathrm{Hz}$. The maximum force in newton, acting on the particle is

EASY

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

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?

MEDIUM

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

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

MEDIUM

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

In an experiment, brass and steel wires of length $1\mathrm{ }\mathrm{m}$ each with areas of cross section $1\mathrm{ }\mathrm{m}{\mathrm{m}}^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of $0.2\mathrm{ }\mathrm{m}\mathrm{m}$ is,
[Given, the Young's Modulus for steel and brass are, respectively, $120\times {10}^9\mathrm{ }\mathrm{N}/{\mathrm{m}}^2$ and $60\times {10}^9\mathrm{ }\mathrm{N}/{\mathrm{m}}^2$ ]

EASY

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

Two separate wires $A$ and $B$ are stretched by $2 \mathrm{mm}$ and $4 \mathrm{mm}$ respectively, when they are subjected to a force of $2 \mathrm{N}.$ Assume that both the wires are made up of same material and the radius of wire $B$ is $4$ times that of the radius of wire $A.$ The length of the wires $A$ and $B$ are in the ratio of $a: b.$ Then $\frac{a}{b}$ can be expressed as $\frac{1}{x}$, where $x$ is _____.

EASY

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

With rise in temperature, young's modulus of elasticity _________.

MEDIUM

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

A body of mass $\mathrm{m}=10 \mathrm{k}\mathrm{g}$ is attached to one end of a wire of length $0.3 \mathrm{m}$. What is the maximum angular speed (in $\mathrm{r}\mathrm{a}\mathrm{d} {\mathrm{s}}^{-1}$) with which it can be rotated about its other end in a space station without breaking the wire?
[Breaking stress of wire $\left(\sigma \right)$$=4.8\times {10}^7 \mathrm{N} {\mathrm{m}}^{-2}$ and area of cross-section of the wire$={10}^{-2} \mathrm{c}{\mathrm{m}}^2$]

EASY

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

A steel wire of cross-sectional area $4 {\mathrm{cm}}^2$ has elastic limit of $2.2\times {10}^8 \mathrm{N} {\mathrm{m}}^{-2}$. The maximum upward acceleration that can be given to a $1000 \mathrm{kg}$ elevator supported by this steel wire if the stress is to exceed one-fourth of the elastic limit is [Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

MEDIUM

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

A boy’s catapult is made of rubber cord which is $42 \mathrm{c}\mathrm{m}$ long, with $6 \mathrm{m}\mathrm{m}$ diameter of cross-section and of negligible mass. The boy keeps a stone weighing $0.02 \mathrm{k}\mathrm{g}$ on it and stretches the cord by $20 \mathrm{c}\mathrm{m}$ by applying a constant force. When released, the stone flies off with a velocity of $20 \mathrm{m}{\mathrm{s}}^{-1}$ . Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:

HARD

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

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

MEDIUM

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

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

MEDIUM

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

The length of a metal wire is $l_1$ when the tension in it is $T_1$ and is $l_2$ when the tension is $T_2$. The natural length of the wire is,

HARD

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

A lift is tied with thick iron ropes having mass $M$. The maximum acceleration of the lift is ‘$a \mathrm{m} {\mathrm{s}}^{-2}$ and maximum safe stress is $S \mathrm{N} {\mathrm{m}}^{-2}$. The minimum diameter of the rope is

EASY

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

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>Elastic Behaviour of Solids

A constant force is applied to a metal wire of length $L$. Volume of the wire is constant. The extension produced is proportional to

MEDIUM

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

Speed of a transverse wave on a straight wire (mass $6.0 \mathrm{g},$ length $60 \mathrm{c}\mathrm{m}$ and area of cross-section $1.0 \mathrm{m}{\mathrm{m}}^2$  is $90 {\mathrm{m} \mathrm{s}}^{-1}$. If the Young's modulus of wire is $16\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$, the extension of wire over its natural length is: