Mechanical properties of solids practice · Medium

A rubber cord catapult has cross-sectional area $25\,\,m{m^2}$ and initial length of rubber cord is $10\,\,cm$. It is stretched to $5\,\,cm$ and then released to project a missile of mass $5\,\,gm$. Taking ${Y_{rubber}} = 5\,\, \times {10^8}\,N/{m^2}$ velocity of projected missile is

Which one of the following quantities does not have the unit of force per unit area

Statement-I: We cannot define Young's modulus and rigidity modulus for liquids and gases.
Statement-II: The theoretical limits of Poisson's ratio are $-1$ to $0.5$

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

Longitudinal strain is possible in

A structural steel rod has a radius of $10 \mathrm{~mm}$ and length of $1.0 \mathrm{~m}$. A $100 \mathrm{kN}$ force stretches it along its length. Young's modulus of structural steel is $2 \times 10^{11} \mathrm{Nm}^{-2}$. The percentage strain is about

A cable that can support a load $w$ is cut into two equal parts. The maximum load that can be supported by either part is

Which of the following elastic moduli is used to describe the elastic behaviour of object as they respond to the deforming forces acting on them?

A copper rod of length 0.19 m is moving with a uniform velocity 10 m/s parallel to a long straight wire carrying current of 5.0 A. The rod itself is perpendicular to wire with its ends at distance 0.01 m and 0.2 m from it. The e.m.f induced in rod is (approximately)

If the interatomic spacing in a steel wire is $3\,{A^\mathrm{o}}\,\,\,\mathrm{ and}\,\,\,\mathrm{ }{y_{\mathrm{steel}}} = 20 \times {10^{10}}N/{m^2}$ then force constant is

Longitudinal stress depends on:

The Young’s modulus of the material of a wire is equal to the

Two bars $A$ and $B$ of circular cross-section and of same volume and made of the same material are subjected to tension. If the diameter of $A$ is half that of $B$ and if the force applied to both the rods is the same and it is in the elastic limit, the ratio of extension of $A$ to that of $B$ will be

If energy acquired per one radian of twist is $\frac{1}{6}\pi J$. The energy acquired by the wire on twisting it for three complete rotations is

Statement I: Ductile metals are used to prepare thin wires.
Statement II: In the stress-strain curve of ductile metals, the length between the points representing elastic limit and breaking point is very small.

Mark the wrong statement

For most materials the Young’s modulus is n times the rigidity modulus, where $n$ is

A) The stretching of a coil is determined by its shear modulus.

B) Of the three states of matter the bulk modulus of elasticity is maximum for gases.

Young's modulus for rigid material is

Statement-1: In general if we apply larger force on a wire in relaxed length it will have larger extension.
Statement-2: Stress is directly proportional to strain if the wire follows Hooke's Law.

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

Identify the incorrect statement.

A steel wire is stretched with a definite load. If the Young’s modulus of the wire is $Y$. For decreasing the value of $Y$

On stretching a wire, the elastic energy stored per unit volume is

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

A material has Poisson's ratio 0.5. If a uniform rod of it suffers a longitudinal strain of $2 \times 10^3$, the percentage increase in its volume is :

Assertion: Steel is more elastic than rubber.

Reason: For same strain, steel requires more stress to be produced in it.

Assertion: Every wire is like a spring, whose spring constant, $K \propto \frac{1}{l}$ where $l$ is length of wire.

Reason: It follows from the relation $K=\frac{Y A}{l}$

The modulus of elasticity is dimensionally equivalent to

The possible value of Poisson’s ratio is