$A$ 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 $F$ is applied on a wire of radius $r$ and length $L$,and the change in the length of the wire is $l$. If the same force $F$ is applied on a wire of the same material with radius $2r$ and length $2L$,then what is the change in the length of the second wire?

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:

In which case is there maximum extension in the wire,if the same force is applied to each wire?

If the interatomic spacing in a steel wire is $3.0 \mathring{A}$ and $Y_{\text{steel}} = 20 \times 10^{10} \text{ N/m}^2$, then the force constant is:

The modulus of elasticity is dimensionally equivalent to