$A$ load of $2 \,kg$ produces an extension of $1 \,mm$ in a wire of $3 \,m$ in length and $1 \,mm$ in diameter. The Young's modulus of the wire will be .......... $Nm^{-2}$.

In an experiment,brass and steel wires of length $1\,m$ each with areas of cross-section $1\,mm^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support,while the other end is subjected to an elongation. The stress required to produce a total elongation of $0.2\,mm$ is: [Given: Young's Modulus for steel and brass are $120 \times 10^9\,N/m^2$ and $60 \times 10^9\,N/m^2$ respectively]

Two wires of the same material have lengths in the ratio $1 : 2$ and their radii are in the ratio $1 : \sqrt{2}$. If they are stretched by applying equal forces,the increase in their lengths will be in the ratio:

The modulus of elasticity is dimensionally equivalent to

$A$ cylindrical rod made of aluminum has a length of $1 \,m$ and a diameter of $10 \,cm$. The rod is subjected to a tensile force of $100 \,kN$. Calculate the elongation in the rod. (Young's modulus of aluminum $= 70 \,GPa$)

$A$ rod of length $L$ and radius $r$ is held between two rigid walls so that it is not allowed to expand. If its temperature is increased,then the force developed in it is proportional to .........