One end of a steel rod of radius $10.0 \ mm$ and length $50.0 \ cm$ is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude $10.0 \times \pi \ kN$. This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (Use Young's modulus $= 2.0 \times 10^{11} \ N/m^2$) (in $mm$)

Which of the following graphs correctly depicts the spring constant $k$ versus the length $l$ of the spring?

Write the equation of bending in a rod. Write the unit of bending and its dimensional formula.

If Young's modulus of iron is $2 \times 10^{11} \ N/m^2$ and the interatomic spacing between two molecules is $3 \times 10^{-10} \ m$,the interatomic force constant is ......... $N/m$.

Which one of the following substances possesses the highest elasticity?

$A$ 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 the radius of the wire is $1 mm$. Assume that $L \gg$ diameter of the wire. Then the value of $m$ in $kg$ is nearly: