If a rod of length $l,$ very small area of cross section $A,$ Young’s modulus of elasticity $Y$ is acted upon by two parallel forces $3F$ and $F$ respectively (as shown) and placed on a smooth horizontal plane. If the elastic limit is not crossed and then to study the change in length of rod $(∆l)$ and it’s elastic potential energy $\left(U\right)$ the rod is segmented into four equal parts where magnitude of change in lengths are$∆l_1, ∆l_2, ∆l_3, ∆l_4$  and elastic potential energy stored in each segment are $U_1, U_2, U_3, U_4$ respectively as shown then which is/are correct?

Two opposite forces $F_1=120 \mathrm{N}$ and $F_2=80 \mathrm{N}$ act on an elastic plank of modulus of elasticity $Y=2\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$ and length $l=1 \mathrm{m}$ placed over a smooth horizontal surface. The cross-sectional area of the plank is $S=0.5{ \mathrm{m}}^2.$ The change in length of the plank is $n\times {10}^{-11} \mathrm{m}.$ Find the value of $n.$

A ring of radius $r$ made of wire of density $\rho$ is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in the figure. Determine the angular velocity (in $\mathrm{rad}/\mathrm{s}$) of ring at which the ring breaks. The wire breaks at tensile stress $\sigma .$ Ignore gravity. Take $\sigma /\rho =4$ and $r=1 \mathrm{m}.$

The bar shown in the figure is made of a single piece of material. It is fixed at one end. It consists of two segments of equal length $L/2$ each but different cross-sectional area $A$ and $2A.$ Find the ratio of total elongation in the bar to the elongation produced in thicker segment under the action of an axial force $F.$ Consider the shape of joint to remain circular. (Given: $Y$ is Young's modulus).

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 $10 \mathrm{mm}.$ How far does the midpoint $A$ move (in $\mathrm{mm}$ )?