$A$ steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^{\circ}C$ so that it cannot contract on cooling. The tension in the rod at $0\,^{\circ}C$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$

Write the unit and dimensional formula of modulus of elasticity.

$A$ 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 ........ $mm$.

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 ........ $mm$.

Two wires of the same material have lengths in the ratio $1:2$ and diameters in the ratio $2:1$. If they are stretched by forces $F_A$ and $F_B$ respectively to produce the same extension,then the ratio $\frac{F_A}{F_B}$ is:

If the ratio of diameters,lengths and Young's moduli of steel and brass wires shown in the figure are $p, q$ and $r$ respectively,then the corresponding ratio of increase in their lengths would be