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 $mm$)

When the temperature of a wire of length $L_0$ is increased by $T$,what is the energy density? The volume expansion coefficient of the wire is $\gamma$ and the Young's modulus is $Y$.

$A$ metal string $A$ is suspended from a rigid support and its free end is attached to a block of mass $M$. $A$ second block having mass $2M$ is suspended at the bottom of the first block using a string $B$. The area of cross-sections of strings $A$ and $B$ are the same. The ratio of lengths of strings $A$ to $B$ is $2$ and the ratio of their Young's moduli $(Y_A/Y_B)$ is $0.5$. The ratio of elongations in $A$ to $B$ is . . . . . . .

Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is $0.5 \ cm$,find the elongation $(l)$ of each wire. Given: ${Y_s} = 2.0 \times {10^{11}} \ N/m^2$ and ${Y_c} = 1.2 \times {10^{11}} \ N/m^2$.

Young's modulus of elasticity of a material depends upon

Two wires $A$ and $B$ of the same material have radii in the ratio $2:1$ and lengths in the ratio $4:1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is .......