To double the length of an iron wire having $0.5 \, cm^2$ area of cross-section,the required force will be $(Y = 10^{12} \, dyne/cm^2)$.

The length of an elastic string is $x \, m$ when the tension is $8 \, N$ and $y \, m$ when the tension is $10 \, N$. The length in meters when the tension is $18 \, N$ is:

$A$ force $F$ is applied on a wire of radius $r$ and length $L$,and the change in the length of the wire is $l$. If the same force $F$ is applied on a wire of the same material with radius $2r$ and length $2L$,then what is the change in the length of the second wire?

$A$ 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 be:

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

What is Young's modulus? Explain it,and provide its unit and dimensional formula.