Water falls from a 40 m high dam at the rate of 9 × 10⁴ kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is :
(Take g = 10 ms⁻²)

Solution

Physics sir · 4 steps

Turn kg per hour into kg per second first; then power is just mgh per second, halved for efficiency.

1. Mass per second. Power is energy per second, so convert the flow rate first: (9 × 10⁴ kg)/(3600 s) = 25 kg s⁻¹.
2. Power from falling water. Each second, 25 kg of water loses potential energy mgh. That rate of energy loss is the input power.

   Pᵢₙ = m/t g h = 25 × 10 × 40 = 10⁴ W

3. Apply efficiency. Only 50% becomes electrical energy, so Pₒᵤₜ = 0.5 × 10⁴ = 5000 W.
4. So. Number of 100 W lamps = 5000/100 = 50, which is option (b).

The idea to keep. For a dam, power is (mass flow per second) × g × h. Always get the flow into kg per second, then multiply by the efficiency before dividing by one lamp's power.

Answer from the NTA final answer key. Solution by PrepWiser.