Water falls from a 40 m high dam at the rate of $$9 \times 10^4$$ kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is
(Take $$g = 10$$ ms$$^{-2}$$)

Water falls from a height $$h = 40$$ m at a rate of $$\frac{dm}{dt} = 9 \times 10^4$$ kg per hour. 50% of gravitational potential energy is converted to electrical energy.

Calculate the gravitational potential energy released per hour.

$$PE = mgh = 9 \times 10^4 \times 10 \times 40 = 3.6 \times 10^7 \text{ J per hour}$$

Convert to power (energy per second).

$$P_{total} = \frac{3.6 \times 10^7}{3600} = 10000 \text{ W} = 10^4 \text{ W}$$

Calculate the electrical power available (50% efficiency).

$$P_{electrical} = 0.5 \times 10^4 = 5000 \text{ W}$$

Find the number of 100 W lamps that can be lit.

$$n = \frac{5000}{100} = 50$$

The correct answer is Option B.