Evaluate the following statements:
$(a)$ Young's modulus of a rigid body is .....
$(b)$ $A$ wire increases by $10^{-6}$ times its original length when a stress of $10^8 \ N/m^2$ is applied to it. Calculate its Young's modulus.
$(c)$ The value of Poisson's ratio for steel is ......

$A$ wire of cross-section $4 \; mm^2$ is stretched by $0.1 \; mm$ by a certain weight. How far (length) will a wire of the same material and length but of area $8 \; mm^2$ stretch under the action of the same force?

$A$ $0.1 \,kg$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \,m$ and its cross-sectional area is $4.9 \times 10^{-7} \,m^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \,rad \,s^{-1}$. If the Young's modulus of the material of the wire is $n \times 10^9 \,N \,m^{-2}$, the value of $n$ is

$A$ steel wire of length $20 \text{ cm}$ and area of cross-section $1 \text{ mm}^2$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \text{C}$ to $20^{\circ} \text{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $\alpha = 1.1 \times 10^{-5} {}^{\circ} \text{C}^{-1}$ and Young's modulus of steel is $Y = 2.0 \times 10^{11} \text{ N/m}^2$. (in $\text{ N}$)

$A$ copper wire of length $2.2 \; m$ and a steel wire of length $1.6 \; m$,both of diameter $3.0 \; mm$,are connected end to end. When stretched by a load,the net elongation is found to be $0.70 \; mm$. Obtain the load applied in $N$.

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?