A steel wire of length ' $L$ ' at $40^{\circ}\,C$ is suspended from the ceiling and then a mass ' $m$ ' is hung from its free end. The wire is cooled down from $40^{\circ}\,C$ to $30^{\circ}\,C$ to regain its original length ' $L$ '. The coefficient of linear thermal expansion of the steel is $10^{-5} { }^{\circ}\,C$, Young's modulus of steel is $10^{11}\, N /$ $m ^2$ and radius of the wire is $1\, mm$. Assume that $L \gg $ diameter of the wire. Then the value of ' $m$ ' in $kg$ is nearly

The interatomic distance for a metal is $3 \times {10^{ – 10}}\,m$. If the interatomic force constant is $3.6 \times {10^{ – 9}}\,N/{{\buildrel _{\circ} \over {\mathrm{A}}}}$, then the Young's modulus in $N/{m^2}$ will be

A copper wire $(Y = 1 \times 10^{11}\, N/m^2)$ of length $6\, m$ and a steel wire $(Y = 2 \times 10^{11}\, N/m^2)$ of length $4\, m$ each of cross section $10^{-5}\, m^2$ are fastened end to end and stretched by a tension of $100\, N$. The elongation produced in the copper wire is ……… $mm$

Read the following two statements below carefully and state, with reasons, if it is true or false.

$(a)$ The Young’s modulus of rubber is greater than that of steel;

$(b)$ The stretching of a coil is determined by its shear modulus.

A load of $2 \,kg$ produces an extension of $1 \,mm$ in a wire of $3 \,m$ in length and $1 \,mm$ in diameter. The Young's modulus of wire will be ………. $Nm ^{-2}$