When a rod is heated but prevented from expanding,the stress developed is independent of

There are two wires of the same material and same length. The diameter of the second wire is two times the diameter of the first wire. What is the ratio of the extensions produced in the wires by applying the same load?

$A$ rod of length $L$ at room temperature and uniform area of cross section $A$ is made of a metal having a coefficient of linear expansion $\alpha /^{\circ}C$. It is observed that an external compressive force $F$,applied on each of its ends,prevents any change in the length of the rod when its temperature rises by $\Delta T \, K$. The Young's modulus $Y$ for this metal is:

The length of a metal wire is found to be $L_1$ and $L_2$ when the tensions $T_1$ and $T_2$ are applied to it respectively. The natural length of the wire is

The ratio of Young's modulus of the material of two wires is $2 : 3.$ If the same stress is applied on both,then the ratio of elastic energy per unit volume will be

Which of the following curves represents the correct distribution of elongation $(y)$ along a heavy rod under its own weight? ($L$ = length of rod, $x$ = distance of a point from the lower end).