Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by forces in the ratio $3: 1$. The ratio of the elastic potential energies stored per unit volume in the wires $A$ and $B$ is

Two wires of equal length and cross-section are suspended as shown. Their Young's moduli are $Y_1$ and $Y_2$ respectively. The equivalent Young's modulus will be

If the ratio of lengths,radii,and Young's moduli of steel and brass wires in the figure are $a, b,$ and $c$ respectively,then the corresponding ratio of increase in their lengths is

In a wire of length $L,$ the increase in its length is $l.$ If the length is reduced to half,the increase in its length will be

Two rods of different materials having coefficients of linear expansion $\alpha_1, \alpha_2$ and Young's moduli $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_1 : \alpha_2 = 2 : 3$,and the thermal stresses developed in the two rods are equal,then the ratio $Y_1 : Y_2$ is equal to:

Which one of the following is not a unit of Young's modulus?