Mechanical properties of solids practice · Mixed difficulty

The modulus of rigidity is also known as:

For a given material, the Young’s modulus is $\mathrm{2}\mathrm{.4}$ times that of modulus of rigidity. Its Poisson’s ratio is

A steel wire of length 40 cm is stretched to increase its length by 0.2 cm. Find the lateral strain in the wire. $\left[ {{\text{if}}\,\,{\text{the}}\,\,\,\sigma = 0.19} \right]$

Given below are two statements: one is labelled as
Assertion A and the other is labelled as Reason R

Assertion A : Steel is used in the construction of
buildings and bridges.

Reason R : Steel is more elastic and its elastic limit
is high.

In the light of above statements, choose the most
appropriate answer from the options given below.

Assertion: The stress-strain behaviour varies from material to material.
Reason: A rubber can be pulled to several times its original length and still returns to its original shape.

A 5 m long aluminium wire $Y = 7 \times {10^{10}}\;\mathrm{N}{\mathrm{m}^{ - 2\;}}$ of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in the copper wire $\left( {Y = 12 \times {{10}^2}\mathrm{Nm}{\mathrm{\;}^{ - 2}}} \right)\;$ of the same length under the same weight, the diameter should now be (in mm)

A copper wire of 4 mm diameter is stretched by applying a force of 20N. Find the stress in the wire [in $N/{m^2}$]

A rubber cord $L$ metre long and having $A \mathrm{~m}^2$ area of cross-section is suspended vertically. If the wire extends $1 \mathrm{~m}$ under its own weight, then change in length $(l)$ is (Take, density of rubber $=D \mathrm{kgm}^{-3}$ and Young's modulus of rubber $=E \mathrm{Nm}^{-2}$ ).

The Young's modulus of a wire is numerically equal to the stress which will

A student plots a graph from his readings on the determination of Young's modulus of a metal wire but forgets to put the labels (figure). The quantities on $\mathrm{X}$ and $\mathrm{Y}$-axes may be respectively

(i) weight hung and length increased

(ii) stress applied and length increased

(iii) stress applied and strain developed

(iv) length increased and the weight hung

A thick rope of rubber of length $8 \mathrm{~m}$ and density $1.5 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ has Young's modulus $5 \times 10^6 \mathrm{Nm}^{-2}$. When hung from ceiling of a room, the increase in length due to its own weight is

Assertion: Bulk modulus of elasticity $(B)$ represents incompressibility of the material.
Reason: Bulk modulus of elasticity is proportional to change in pressure.

Statement I: The bridges declared unsafe after a long use.
Statement II: Elastic strength of bridges loses with time.

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

A wire suspended vertically from one of its ends is stretched by attaching a weight of $250 \mathrm{~N}$ to the lower end. The weight stretches the wire by $2 \mathrm{~mm}$. Then the elastic energy stored in the wire is:

A rubber ball is taken to a $100 \mathrm{~m}$ deep lake and its volume changes by $0.1 \%$. The bulk modulus of rubber is nearly:

The Young’s modulus of brass and steel are $10 \times {10^{10}}\,\mathrm{N}{\mathrm{m}^{ - 2}}\,\,\mathrm{and}\,\,2 \times {10^{11}}\,\mathrm{N}{\mathrm{m}^{ - 2}}$ respectively. A brass wire and a steel wire of the same length are extended by $\mathrm{1 mm}$ under the same force. The radii of the brass and steel wires are ${R_B}\,\,and\,\,{R_S}$ respectively. Then

A plate having a circular hole is heated and allowed freely to expand. Mark the incorrect statement

What will be energy stored in a strained wire?

The elastic energy stored in a wire of Young’s modulus $Y$ is

Statement-I: The product of bulk modulus of elasticity and compressibility is one.
Statement-II: Tangential stress applied on the body only produces change in shape but not in size.

When a rubber cord is stretched, the change in volume with respect to change in its linear dimensions is negligible. The Poisson’s ratio for rubber is

The Bulk modulus for an incompressible liquid is

Two wires of the same material, have radii and lengths are both in the ratio $1: 2$. If the extensions produced are equal, what is the ratio of loads ?

Assertion: In spring ball model, displace any ball from its equilibrium position the spring system tries to restore the ball back to its original position.
Reason: The elastic behaviour of solids can be explained in terms of microscopic nature of the solid.

The length of a wire under stress changes by $0.01\%$. The strain produced is

The possible value of Poisson’s ratio is

What per cent of length of wire increases by applying a stress of $1 \mathrm{~kg}$ weight $/ \mathrm{mm}^2$ on it?

$\left(\mathrm{Y}=1 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\right.$ and $1 \mathrm{~kg}$ weight $=9.8$ newton $)$

A sphere contracts in volume by $0.02 \%$, when taken to the bottom of sea $1 \mathrm{~km}$ deep. The bulk modulus of the material of the sphere is: (Given density of sea water may be taken as $1.0 \times 10^3 \mathrm{~kgm}^{-3}$)

Only volumetric strain can be developed in case of: