Elasticity Questions

A wire fixed at the upper end stretches by length $l$ by applying a force $F$. The work done in stretching is:

A wire elongates by $\ell \text{mm}$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in mm):

If $S$ is stress and $Y$ is Young’s modulus of material of a wire, the energy stored in the wire per unit volume is:

A wire suspended vertically from one of its ends stretched by attaching weight of $200\text{N}$ to the lower end. The weight stretches the wire by $1\text{mm}$. Then the elastic energy stored in the wire is:

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area $A$ and wire-2 has cross-sectional area $3A$. If the length of wire 1 increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire 2 by the same amount?

A wooden wheel of radius $R$ is made of two semicircular parts. The two parts are held together by a ring made of a metal strip of cross sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Young's modulus is $Y$, the force that one part of the wheel applies on the other part is: