If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $$\alpha \mathrm{h}\left(\mathrm{h}<<\mathrm{R}_{\mathrm{e}}\right)$$ from the earth surface. The value of $$\alpha$$ will be _________.

(use $$\left.\mathrm{R}_{\mathrm{e}}=6400 \mathrm{~km}\right)$$

The pressure $$\mathrm{P}_{1}$$ and density $$\mathrm{d}_{1}$$ of diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ changes suddenly to $$\mathrm{P}_{2}\left(>\mathrm{P}_{1}\right)$$ and $$\mathrm{d}_{2}$$ respectively during an adiabatic process. The temperature of the gas increases and becomes ________ times of its initial temperature. (given $$\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}=32$$)

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $$\frac{\alpha^{2}}{4} \mathrm{R} \,\mathrm{J} / \mathrm{mol} \,\mathrm{K}$$; then the value of $$\alpha$$ will be _________. (Assume that the given diatomic gas has no vibrational mode).

The current I flowing through the given circuit will be __________A.