$A$ steel rod of length $1\,m$ and area of cross-section $1\,cm^2$ is heated from $0\,^{\circ}C$ to $200\,^{\circ}C$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.

What is the effect of change in temperature on the Young's modulus?

The area of a cross-section of a steel wire is $0.1 \, cm^2$ and Young's modulus of steel is $2 \times 10^{11} \, N \, m^{-2}$. The force required to stretch it by $0.1 \%$ of its original length is ......... $N$.

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$,the force with which the metal ring expands is

$A$ block of mass $2 \ kg$ is tied to one end of a $2 \ m$ long metal wire of $1.0 \ mm^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is $2 \ mm$,the Young's modulus of the metal is (Acceleration due to gravity $= 10 \ ms^{-2}$)

$A$ sphere of mass $2 \,kg$ and diameter $4.5 \,cm$ is attached to the lower end of a steel wire of $2 \,m$ length and area of cross-section $0.24 \times 10^{-6} \,m^2$. The wire is suspended from a $205 \,cm$ high ceiling of a room. When the system is made to oscillate as a simple pendulum, the sphere just grazes the floor at its lowest position. Find the velocity of the sphere at the lowest position. (Young's modulus of steel $= 2 \times 10^{11} \,Nm^{-2}$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-1}$)