When a certain weight is suspended from a long uniform wire,its length increases by $1 \ cm$. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one,then the increase in length will be ........ $cm$.

$A$ steel wire is stretched with a definite load. If the Young's modulus of the wire is $Y$,how can the value of $Y$ be decreased?

Two blocks of mass $2 \ kg$ and $4 \ kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The radius of the wire is $4.0 \times 10^{-5} \ m$ and Young's modulus of the metal is $2.0 \times 10^{11} \ N/m^2$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi}$. The value of $\alpha$ is [Use $g = 10 \ m/s^2$].

$A$ $3 \ m$ long wire of radius $3 \ mm$ shows an extension of $0.1 \ mm$ when loaded vertically by a mass of $50 \ kg$ in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $P \times 10^{11} \ Nm^{-2}$,where the value of $P$ is: (Take $g = 3 \pi \ m/s^2$)

$A$ wire of length $2\, m$ is made from $10\, cm^3$ of copper. $A$ force $F$ is applied so that its length increases by $2\, mm$. Another wire of length $8\, m$ is made from the same volume of copper. If the same force $F$ is applied to it,its length will increase by ......... $cm$.

Young's modulus of elasticity of a material depends upon