Mechanical properties of solids practice · Mixed difficulty

Copper of fixed volume ' $\mathrm{V}$; is drawn into wire of length ' $l$ '. When this wire is subjected to a constant force ' $\mathrm{F}$ ', the extension produced in the wire is ' $\Delta l$ '. Which of the following graphs is a straight line?

A: Spring balances show wrong readings after they have been used for a long time.
R: Spring in spring balance temporary losses elasticity due to repeated alternating deforming force.

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 the length of a wire is reduced to half, then it can hold the Load

A: Bulk modulus for a perfectly plastic body is zero.
R: For perfect plastic material, there is no restoring force.

The expression of force constant for a spring following Hooke's law is given by:

Statement-I: When the length of a wire is doubled, the Young's modulus of the wire is also doubled
Statement-II: For elastic bodies Poisson ratio is +Ve; for inelastic bodies Poisson ratio is -Ve

A: Hooke's law is obeyed only for small values of strain.
R: The deformation beyond elastic limit is called plasticity.

Which one of the following statements is correct? In the case of

If the temperature increases, the modulus of elasticity:

A wire is elongated by an external force which is always equal to restoring force developed in the wire material. $W$ work is done by the external force in elongating wire by $x$ unit then energy of wire increases by

A rubber cord $10m$ long is suspended vertically. How much does it stretch under its own weight (Density of rubber is $1500\;kg/{m^3},Y = 5 \times {10^8}N/{m^2},g = 10\;m/{s^2})$

A uniform cube is subjected to volume compression. If each side is decreased by $1\,\,\%$, then bulk strain is

Assertion: A piece of metal wire will elongate when subjected to a tensile force.

Reason: When a tensile force is applied to a metal wire, the interatomic spacing between the atoms in the wire increases.

A: To minimize the depression in a beam, it is designed as '${I}$' shape girder.
R: The '$I$' shape girders have large load bearing surface, which decreases the stress

Steel is preferred for making spring over
copper. Why?

On increasing temperature, the elasticity of a material

A metal wire of length $L,$ area of cross section $A$ and Young's modulus $Y$ behaves as a spring of spring constant $k$ given by:

The breaking stress of aluminium is $7.5 \times 10^8$ dyne $\mathrm{cm}^{-2}$. Find the greatest length of aluminium wire that can hang vertically without breaking. Density of aluminium is $2.7 \mathrm{~g} \mathrm{~cm}^{-3}$. [Given : $\mathrm{g}=980 \mathrm{~cm~s}^{-2}$ ]

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

Let $Y_{{S}}$ and $Y_{{A}}$ represent Young's modulus for steel and aluminium respectively. It is said that steel is more elastic than aluminium. Therefore, it follows that:

A cylindrical wire is twisted with an angle $\theta$, what is torsion produced in it?

The breaking stress for a wire of unit cross-section is called:

A cylindrical wire having radius $1 \mathrm{~cm}$ and length $10 \mathrm{~cm}$ is twisted by an angle $\frac{\pi}{60}$ radian, then find shear strain produced in the wire.

Statement-I: The bulk modulus for an incompressible liquid is infinite.
Statement-II: Young's modulus increases with rise of temperature.

If longitudinal strain for a wire is $\mathrm{0}\mathrm{.03}$ and its Poisson’s ratio is $\mathrm{0}\mathrm{.5}$, then its lateral strain is

Assertion: Bulk modulus of elasticity can be defined for all three states of matter, solid liquid and gas.

Reason: Young's modulus is not defined for liquids and gases.

The bulk modular of an ideal rigid substance is.

Which of the following statements is correct

Two wires of copper having the length in the ratio 4:1 and their radii ratio as 1:4 are stretched by the same force. The ratio of longitudinal strain in the two will be