Mechanical properties of solids practice · Mixed difficulty

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 ?

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

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 $1 \mathrm{~m}$ long and $1 \mathrm{~mm}^2$ in area of crosssection. If it takes $200 \mathrm{~N}$ to stretch this wire by $1 \mathrm{~mm}$, how much force will be required to stretch a wire of the same material as well diameter from its normal length of $10 \mathrm{~m}$ to a length of $1002 \mathrm{~cm}$ ?

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

Two forces $F_1$ and $F_2$ are applied on two rods $P$ and $Q$ of same materials such that elongation in rods are same. If ratio of their radii is $x$ : $y$ and ratio of length is $m: n$, then ratio of $F_1: F_2$ is

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

If to break a wire of $1 \mathrm{~m}$ length, minimum $40 \mathrm{~kg}$-wt is required, then to break a wire of same material $6 \mathrm{~m}$ in length and double in radius, the breaking weight required will be

A wire of length '$2 \mathrm{~m}$' is clamped horizontally between two fixed support. A mass $\mathrm{m}=5 \mathrm{~kg}$ is hanged from middle of wire. The vertical and depression in wire (in $\mathrm{cm}$) in equilibrium is (Young modulus of wire $=2.4 \times 10^9 \mathrm{~N} / \mathrm{m}^2$, cross-sectional area $=1 \mathrm{~cm}^2$)

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?

A copper wire $\left(Y=10^{11} \mathrm{Nm}^{-2}\right)$ of length $8 \mathrm{~m}$ and a steel wire $\left(Y=2 \times 10^{11} \mathrm{Nm}^{-2}\right)$ of length $4 \mathrm{~m}$, each of $0.5 \mathrm{~cm}^2$ cross-section are fastened end-to-end and stretched with a tension of $500 \mathrm{~N}$. Choose the correct statement.

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.

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

Steel is preferred for making spring over
copper. Why?

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