In an experiment to determine the Young's modulus, steel wires of five different lengths $(1,2,3,4$ and $5\,m )$ but of same cross section $\left(2\,mm ^{2}\right)$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11}\,Nm ^{-2}$, then the value of $x$ is

Young's modulus of rubber is ${10^4}\,N/{m^2}$ and area of cross-section is $2\,c{m^2}$. If force of $2 \times {10^5}$ dynes is applied along its length, then its initial length $l$ becomes

A meter scale of mass $m$ , Young modulus $Y$ and cross section area $A$ is hanged vertically from ceiling at zero mark. Then separation between $30\  cm$ and $70\  cm$ mark will be 🙁 $\frac{{mg}}{{AY}}$ is dimensionless) 

A steel wire of diameter $2 \,mm$ has a breaking strength of $4 \times 10^5 \,N$.the breaking force ……… $\times 10^5 \,N$ of similar steel wire of diameter $1.5 \,mm$ ?

A boy’s catapult is made of rubber cord which is $42\, cm$ long, with $6\, mm$ diameter of cross -section and of negligible mass. The boy keeps a stone weighing $0.02\, kg$ on it and stretches the cord by $20\, cm$ by applying a constant force. When released, the stone flies off with a velocity of $20\, ms^{-1}$. Neglect the change in the area of cross section of the cord while stretched. The Young’s modulus of rubber is closest to