$A$ brass wire of length $2 \ m$ and radius $1 \ mm$ at $27 ^\circ C$ is held taut between two rigid supports. Initially, it was cooled to a temperature of $-43 ^\circ C$, creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4 \ T$ is . . . . . . $^\circ C$.

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$, the force with which the metal ring expands is

$A$ force of $200\, N$ is applied at one end of a wire of length $2\, m$ and having area of cross-section $10^{-2}\, cm^2$. The other end of the wire is rigidly fixed. If the coefficient of linear expansion of the wire is $\alpha = 8 \times 10^{-6}\, ^\circ C^{-1}$,Young's modulus is $Y = 2.2 \times 10^{11}\, N/m^2$,and its temperature is increased by $5\, ^\circ C$,then the increase in the tension of the wire will be ........ $N$.

$A$ bar is subjected to axial forces as shown. If $E$ is the modulus of elasticity of the bar and $A$ is its cross-section area,its total elongation will be:

The units of Young's modulus of elasticity are

$A$ $14.5\; kg$ mass,fastened to the end of a steel wire of unstretched length $1.0\; m$,is whirled in a vertical circle with an angular velocity of $2\; rev/s$ at the bottom of the circle. The cross-sectional area of the wire is $0.065\; cm^2$. Calculate the elongation of the wire when the mass is at the lowest point of its path.