A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of rope is $Y$. The increase in length of the rope due to its own weight is

Each of three blocks $P$, $Q$ and $R$ shown in figure has a mass of $3 \mathrm{~kg}$. Each of the wire $A$ and $B$ has cross-sectional area $0.005 \mathrm{~cm}^2$ and Young's modulus $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is____________ $\times 10^{-4}$. $\left(\right.$ Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

Explain experimental determination of Young’s modulus.

Young's modulus is determined by the equation given by $\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}$ where $\mathrm{M}$ is the mass and $\ell$ is the extension of wre used in the experiment. Now error in Young modules $(\mathrm{Y})$ is estimated by taking data from $M-\ell$ plot in graph paper. The smallest scale divisions are $5 \mathrm{~g}$ and $0.02$ $\mathrm{cm}$ along load axis and extension axis respectively. If the value of $M$ and $\ell$ are $500 \mathrm{~g}$ and $2 \mathrm{~cm}$ respectively then percentage error of $\mathrm{Y}$ is :

Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is $0.5$ cm, the elongation $(l)$ of each wire is ${Y_s}({\rm{steel}}) = 2.0 \times {10^{11}}\,N/{m^2}$${Y_c}({\rm{copper}}) = 1.2 \times {10^{11}}\,N/{m^2}$

A steel wire of length $3.2 m \left( Y _{ S }=2.0 \times 10^{11}\,Nm ^{-2}\right)$ and a copper wire of length $4.4\,M$ $\left( Y _{ C }=1.1 \times 10^{11}\,Nm ^{-2}\right)$, both of radius $1.4\,mm$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4\,mm$. The load applied, in Newton, will be. (Given $\pi=\frac{22}{7}$)