Water descending from a 50 m high fall is utilized to generate electric energy. If 1.8 10^5 kg of water falls per hour and half of the gravitational potential energy can be converted into electric energy, determine how many 100 W lamps can be lit.

Step-by-step solution

Mass of water falling per second, m t = 1.8 10^5 3600 = 50 kg/s Total power available from the falling water is P = mgh t Taking g = 10 m/s ^2 , we get: P = 50 10 50 = 25000 W Electric power generated is half of the available power: P_ elec = 25000 2 = 12500 W Number of 100 W lamps that can be lit is: n = 12500 100 = 125