Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$. How far does the midpoint $A$ move ………… $mm$

Which of the following curve represents the correctly distribution of elongation $(y)$ along heavy rod under its own weight $L \rightarrow$ length of rod, $x \rightarrow$ distance of point from lower end?

A wire of cross sectional area $A$, modulus of elasticity $2 \times 10^{11} \mathrm{Nm}^{-2}$ and length $2 \mathrm{~m}$ is stretched between two vertical rigid supports. When a mass of $2 \mathrm{~kg}$ is suspended at the middle it sags lower from its original position making angle $\theta=\frac{1}{100}$ radian on the points of support. The value of $A$ is. . . . . .  $\times 10^{-4} \mathrm{~m}^2$ (consider $\mathrm{x}<\mathrm{L}$ ).

(given: $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

A uniformly tapering conical wire is made from a material of Young's modulus $Y$  and has a normal, unextended length $L.$ The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R,$  respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal 

In which case there is maximum extension in the wire, if same force is applied on each wire