A certain wire $$\mathrm{A}$$ has resistance $$81 ~\Omega$$. The resistance of another wire $$\mathrm{B}$$ of same material and equal length but of diameter thrice the diameter of A will be :
$$\epsilon_0$$ and $$\mu_0$$ are the electric permittivity and magnetic permeability of free space respectively. If the corresponding quantities of a medium are $$2 ~\epsilon_0$$ and $$1.5 ~\mu_0$$ respectively, the refractive index of the medium will nearly be :
The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length $$100 \mathrm{~cm}$$ to stretch it by $$1 \mathrm{~mm}$$ is (if Young's modulus of the wire $$=2.0 \times 10^{11} \mathrm{Nm}^{-2}$$ ) :
The $$4^{\text {th }}$$ overtone of a closed organ pipe is same as that of $$3^{\text {rd }}$$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is :