In a wire of length $L,$ the increase in its length is $l.$ If the length is reduced to half,the increase in its length will be

$A$ steel rod of radius $20 \ mm$ and length $2 \ m$ is acted upon by a force of $400 \ kN$ along its length. The values of stress and strain are respectively $(Y_{\text{steel}} = 2 \times 10^{11} \ N \ m^{-2})$.

Young's moduli of the material of wires $A$ and $B$ are in the ratio of $1: 4$,while their areas of cross-section are in the ratio of $1: 3$. If the same amount of load is applied to both the wires,the amount of elongation produced in the wires $A$ and $B$ will be in the ratio of [Assume length of wires $A$ and $B$ are same].

$A$ metal rod of Young's modulus $Y$ and coefficient of linear expansion $\alpha$ has its temperature raised by $\Delta \theta$. The linear stress required to prevent the expansion of the rod is:

Two wires made of the same material are clamped rigidly at one end and pulled by the same force on the other end. The length and the radius of the first wire are three times those of the second wire. If $x$ is the increase in the length of the first wire,then the increase in the length of the second wire is

Increase in length of a wire is $1 \, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius,the increase in length will be ........ $mm$.