In a capillary tube of radius 'R', a straight thin metal wire of radius 'r' is inserted symmetrically and one end of the combination is dipped vertically in water such that lower end of the capillary and thin wire are at same level. If 'T' is the surface tension of water and '$\rho$' is the density of water then the rise of water in the capillary is

Due to surface tension, the excess pressure inside a smaller drop is $9$ units. If $27$ smaller drops combine then excess pressure inside the bigger drop is

A body cools in $7$ minutes from $60^\circ$C to $40^\circ$C. What time (in minutes) does it take to cool from $40^\circ$C to $28^\circ$C, if its surrounding temperature is $10^\circ$C ? (Newton's law of cooling holds good)

A rigid diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as $P \propto T^x$ where x is