Mechanical properties of solids practice · Medium

Dimensions of stress are

Statement I: A steel wire of natural length '$\ell$' breaks, when clongated by length '$x$'. If original length is halved and elongated by $x / 2$ it breaks.
Statement II: Breaking force is directly proportional to the length of the wire.

A uniform wire, fixed at its upper end, hangs vertically and supports a weight at its lower end. If its radius is $r$, its length $L$ and the Young’s modulus for the material of the wire is $E$, the extension is
1. directly proportional to $E$

2. inversely proportional to $r$

3. directly proportional to $L$

Assertion: Steel is more elastic than rubber.
Reason: Under given deforming force, steel is deformed less than rubber.

Assertion: Rise in temperature of a material causes decrease in the elasticity of the material.
Reason: The presence of impurities always increases the elasticity of the material.

A stress of $3.18\,\, \times {10^8}N{m^{ - 2}}$ is applied to a steel rod of length $1\,\,m$ along its length. Its Young’s modulus is $2\,\, \times \,\,{10^{11}}N{m^{ - 2}}$. Then the elongation produced in the rod in $mm$ is

An elevator cable is to have a maximum stress of $7 \times 10^7 \mathrm{Nm}^{-2}$ to allow for appropriate safety factors. Its maximum upward acceleration is $1.5 \mathrm{~ms}^{-2}$. If the cable has to support the total weight of $2000 \mathrm{~kg}$ of a loaded elevator, the area of cross-section of the cable should be

If the load is increased beyond the _____ point, the strain increases rapidly for even a small change in the stress.

A: Lateral strain is directly proportional to the longitudinal strain within the elastic limit.
R: Poisson's ratio for a given material at a constant temperature is constant.

In a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of longitudinal strain $\sigma$ and modulus of elasticity $Y$ is

Which of the following relation is true?

A solid sphere of radius $10 \mathrm{~cm}$ is subjected to a uniform pressure $=5 \times 10^8 \mathrm{~Nm}^{-2}$. Determine the consequent change in volume. Bulk modulus of the material of the sphere is equal to $3.14 \times 10^{11} \mathrm{~Nm}^{-2}$.

In which year Robert Hooke presented his law of elasticity?

Shape is related to:

Assertion: Rigid body can be elastic.
Reason: If a force is applied on the rigid body, its dimension may change.

The elastic limit of brass is $379MPa$. What should be the minimum diameter of a brass rod, if it is to support a $400N$ load without exceeding its elastic limit

Statement-I: Young's modulus, bulk modulus and shear modulus have the units of pressure.
Statement-II: The value of Young's modulus depends area of body.

Within proportional limit, the slope of the stress stain curve yields,

The Young’s modulus of a wire of length $L$ and radius $r$ is $Y\mathrm{ }N/{m^2}$. If the length and radius are reduced to $L/2$ and $r/2$, then its Young’s modulus will be

Which of the following substances has the highest elasticity?

Statement I: Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Both the balls will rise to same height after bouncing.
Statement II: Ivory and wet-clay have same elasticity.

A stretched rubber has

Statement I: Silver is a ductile material,
Statement II: For a ductile material yield point and breaking point are separated by larger distance than for brittle materials on the stress-strain curve.

Bulk modulus of a material, whose Poison's ratio equal to 0.5 is

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: