Two spherical conductors of radii $$4 \mathrm{~cm}$$ and $$5 \mathrm{~cm}$$ are charged to the same potential. If '$$\sigma_1$$' and '$$\sigma_2$$' be the respective values of the surface density of charge on the two conductors then the ratio $$\sigma_1: \sigma_2$$ is

Kirchhoff's current and voltage law are respectively based on the conservation of

A glass tube of $$1 \mathrm{~m}$$ length is filled with water. The water can be drained out slowly from the bottom of the tube. If vibrating tuning fork of frequency $$500 \mathrm{~Hz}$$ is brought at the upper end of the tube then total number of resonances obtained are [Velocity of sound in air is $$320 \mathrm{~ms}^{-1}$$]

The rate of flow of heat through a copper rod with temperature difference $$28^{\circ} \mathrm{C}$$ is $$1400 \mathrm{~cal} \mathrm{~s}^{-1}$$. The thermal resistance of copper rod will be