A person decides to use bath tub water to generate electric power to run a 40 W bulb. The bath tub is located at a height of 10 m from the ground and it holds 200 liters of water. He installs a water driven wheel generator on the ground. At what rate should the water drain from the bath tub to light the bulb? The density of water is `1000(kg)//(m^3)` and efficiency of generator is `80%`. How long can he keep the bulb on if the bath tub was full initially.

Explanation

Efficiency`=(output power)/(I nput power)implies(80)/(100)=(40)/(P_0)impliesP_0=50W`
`P_0=(W)/(t)=(mgh)/(t)=(mxx10xx10)/(t)`
`50=(m)/(t)xx100implies(m)/(t)=0.5`
Rate at which falling/second`=0.5(kg)//(s)`
Mass of water in tub `=rhoV=10^3xx200xx10^-3=200kg`
(`1litre=10^-3m^3`)
Time of which bulb is on `=(200)/(0.5)=400s`