Mechanical properties of solids practice · Medium

A force $F$ is required to break a wire of length $I$ and radius $r$. What force is required to break a wire, of the same material, having twice the length and six times the radius ?

A metal wire of length $L$ is suspended vertically from a rigid support. When a body of mass $M$ is attached to the lower end of wire, the elongation of the wire is $\ell$, then the incorrect statement is

Young’s modulus of perfectly rigid body material is

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

The specific heat at constant pressure and at constant volume for an ideal gas are ${C_p}$ and ${C_v}$ and its adiabatic and isothermal elasticities are ${E_\phi }$ and ${E_\theta }$ respectively. The ratio of ${E_\phi }$ to ${E_\theta }$ is

Which of the following statements is/are wrong?
I. Hollow shaft is much stronger than a solid rod of same length and same mass
II. Reciprocal of bulk modulus of elasticity is called compressibility
III. It is difficult to twist a long rod as compared to small rod.

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

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

A load suspended by a massless spring produces an extension of $x\,\,cm$ in equilibrium. When it is cut into two unequal parts, the same load produces an extension of $7.5\,\,cm$ when suspended by the larger part of length 60 cm. When it is suspended by the smaller part, the extension is 5.0 cm Then

Given below are two statements : One is labelled as, Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason (R) : A coil spring of copper has more tensile strength than a steel spring of same dimensions.
In the light of the above statements, choose the most, appropriate answer from the options given below

If the length of a wire is made double and radius is
halved of its respective values. Then, the Young's
modulus of the material of the wire will :

Assertion: If length of a rod is doubled, the breaking load remains the same.
Reason: Breaking load is equal to the elastic limit.

Two rods of copper and steel having same area of cross - section but different lengths $l_{1}$ and $l_{2}$ respectively are connected to each other. The combined length of two rods fits between two walls without any stress on walls. If $\alpha_{1}$ and $\alpha_{2}$ are their coefficient of linear expansion, $Y_{1}$ and $Y_{2}$ are their Young's modulus respectively, then (There is no buckling of rods while heating) With increase in temperature:

In above question, the work done in the two wires is

A wire is stretched $1\mathrm{ }mm$ by a force of $1\mathrm{ }k\mathrm{ }N$. How far would a wire of the same material and length but of four times that diameter be stretched by the same force ?

Forces of 100 N each are applied in opposite directions on the upper and lower faces of a cube of side $20\,cm$. The upper face is shifted parallel to itself by $0.25\,cm$. If the side of the cube were 10 cm, then the displacement would be

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

Mark the wrong statement

Two spring $P$ and $Q$ of force constants ${k_p}$ and ${k_Q}\left( {{k_Q} = \frac{{{k_p}}}{2}} \right)$ are stretched by applying forces of equal magnitude if the energy stored in $Q$ is $E$, then the energy stored in $P$ is

Two wires of same material and radius have their lengths in ratio $1:2$. If these wires are stretched by the same force, the strain produced in the two wires will be in the ratio

Assertion: From the relation $Y=\frac{F l}{A \Delta l},$ we can say that, if length of a wire is doubled, its Young's modulus of elasticity will also becomes two times.

Reason: Modulus of elasticity is a material property.

Statement-I: Rigidity modulus of a liquid is infinity
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.

Which statement is true for a metal

To break a wire of one metre length, minimum $40\;kg\;wt$, is required. Then the wire of the same material of double radius and 6 m length will require breaking weight

Which of the following relation is true?

The modulus of elasticity is dimensionally equivalent to

A: Equal amount of work is done when two identical springs of steel and copper are equally streched
R: Both springs have same spring constant.

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

If a wire is stretched such that its length becomes double then

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.