The velocity ‘v’ of water waves depends on the wavelength ‘λ’, density of water ‘ρ’ and acceleration due to gravity ‘g’. Deduce the expression for velocity and show that velocity varies with 1/2 th power of wavelength.

Name two kinds of practical electric pumps.

Along wire of diameter 1 mm is submerged in an oil bath of temperature ∞ 31°c. the wire has an electrical resistance per unit length of 0.01 ω/m. if a current of 103 a flows through the wire and the convection coefficient is 500 w/m2·k, what is the steady-state temperature of the wire? from the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°c of the steady-state value? the properties of the wire are 8000 kg/m3, 500 j/kg·k, and 20 w/m·k.

The largest observatory complex in the world is on mauna kea, the tallest mountain on earth. what are some factors astronomers consider when selecting an observatory site? don’t forget practical ones. should astronomers, for example, consider building an observatory on denali (mount mckinley) or mount everest?