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The length of a metal wire is $l_1$ when the tension in it is $F_1$ and $l_2$ when the tension is $F_2$. Then,the original length of the wire is

Match the physical quantities in Column-$I$ with the details given in Column-$II$ appropriately:
Column-$I$ Column-$II$
$(a)$ $\text{Stress} \propto \text{Strain}$ $(i)$ $M^1 L^{-1} T^{-2}$
$(b)$ $\text{Dimensional formula for compressibility}$ $(ii)$ $M^{-1} L^1 T^2$
$(iii)$ $\text{Poisson's ratio}$
$(iv)$ $\text{Hooke's law}$

$A$ rod of length $2 \ m$ rests on a smooth horizontal floor. If the rod is heated from $0^\circ C$ to $20^\circ C$,find the longitudinal strain developed? $(\alpha = 5 \times 10^{-5} / ^\circ C)$

The breaking stress for a wire of radius $r$ of a given material is $F \ Nm^{-2}$. The breaking stress for a wire of the same material of radius $2r$ will be:

$A$ force of $10 \,N$ is required to break a wire of radius $1 \,mm$. The force required to break the wire of the same material, but radius $3 \,mm$ will be

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