The length of a wire becomes $l_1$ and $l_2$ when $100\,N$ and $120\,N$ tensions are applied respectively. If $10l_2 = 11l_1$,the natural length of the wire will be $\frac{1}{x} l_1$. Here,the value of $x$ is ........

The speed of a transverse wave travelling in a wire of length $50 \text{ cm}$,cross-sectional area $1 \text{ mm}^2$ and mass $5 \text{ g}$ is $80 \text{ ms}^{-1}$. The Young's modulus of the material of the wire is $4 \times 10^{11} \text{ Nm}^{-2}$. The extension in the length of the wire is

If $\delta$ is the depression produced in a beam of length $L$,breadth $b$ and thickness $d$,when a load $W$ is placed at the mid-point,then:

$A$ rod of length $l$ and area of cross-section $A$ is heated from $0^{\circ}C$ to $100^{\circ}C$. The rod is so placed that it is not allowed to increase in length,then the force developed is proportional to

At $40\,^oC$,a brass wire of radius $0.5\, mm$ (diameter $1\, mm$) is hung from the ceiling. $A$ small mass $M$ is hung from the free end of the wire. When the wire is cooled down from $40\,^oC$ to $20\,^oC$,it regains its original length of $0.2\, m$. The value of $M$ is close to ........$kg$. (Coefficient of linear expansion $\alpha = 10^{-5}/^oC$ and Young's modulus $Y = 10^{11}\, N/m^2$; $g = 10\, ms^{-2}$)

The following four wires are made of the same material. Which one will have the largest elongation when subjected to the same tension?