The density of a metal at normal pressure $$p$$ is $$\rho$$. When it is subjected to an excess pressure, the density becomes $$\rho^{\prime}$$. If $$K$$ is the bulk modulus of the metal, then the ratio $$\frac{\rho^{\prime}}{\rho}$$ is

Two rods of same material and volume having circular cross-section are subjected to tension $$T$$. Within the elastic limit, same force is applied to both the rods. Diameter of the first rod is half of the second rod, then the extensions of first rod to second rod will be in the ratio

For homogeneous isotropic material, which one of the following cannot be the value of Poisson's ratio?

A wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$, the increase in length is $I$. If another wire of the same material but double the length and radius is stretched with a force $2 F$, then increase in length is