Two metallic wires $P$ and $Q$ have the same volume and are made up of the same material. If their areas of cross-section are in the ratio $4:1$ and a force $F_1$ is applied to $P$,an extension of $\Delta l$ is produced. The force required to produce the same extension in $Q$ is $F_2$. The value of $\frac{F_1}{F_2}$ is . . . . . . .

$A$ 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

$A$ 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?

The length of a light string is $1.4 \ m$ when the tension on it is $5 \ N$. If the tension increases to $7 \ N$,the length of the string is $1.56 \ m$. The original length of the string is . . . . . . $m$.

$A$ load of mass $M \ kg$ is suspended from a steel wire of length $2 \ m$ and radius $1.0 \ mm$ in Searle's apparatus experiment. The increase in length produced in the wire is $4.0 \ mm$. Now,the load is fully immersed in a liquid of relative density $2$. The relative density of the material of the load is $8$. The new value of increase in length of the steel wire is ........ $mm$.

Young's modulus of the material of a wire of length $L$ and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and the cross-sectional area is halved,then the Young's modulus will be: