$A$ steel wire of length $3 \ m$ and a copper wire of length $2.2 \ m$ are connected end to end. When the combination is stretched by a force,the net elongation is $1.05 \ mm$. If the area of cross-section of each wire is $6 \ mm^2$,then the load applied is (Young's modulus of steel and copper are respectively $2 \times 10^{11} \ N/m^2$ and $1.1 \times 10^{11} \ N/m^2$) (in $N$)

As shown in the figure,a light uniform rod $PQ$ of length $150 \ cm$ is suspended from the ceiling horizontally using two metal wires $A$ and $B$ tied to the ends of the rod. The ratios of the radii and the Young's moduli of the materials of the two wires $A$ and $B$ are respectively $2:3$ and $3:2$. The position at which a weight should be suspended from the rod such that the elongations of the two wires become equal is

The mean distance between the atoms of iron is $3 \times 10^{-10} \ m$ and the interatomic force constant for iron is $7 \ N/m$. The Young's modulus of elasticity for iron is:

$A$ rod of length $1000\, mm$ and coefficient of linear expansion $\alpha = 10^{-4} / ^\circ C$ is placed symmetrically between fixed walls separated by $1001\, mm$. The Young's modulus of the rod is $10^{11} N/m^2$. If the temperature is increased by $20^\circ C$,then the stress developed in the rod is ........... $MPa$.

$A$ force of $10^3 \ N$ stretches the length of a hanging wire by $1 \ mm$. The force required to stretch a wire of the same material and length,but having four times the diameter,by $1 \ mm$ is:

If the ratio of length,radii,and Young's modulus of steel and aluminium wire are $a, b, c$ respectively,then the corresponding ratio of increase in their length would be: