Question

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 hydro electric energy number of 100 W lamps, that can be lit, is :
(Take g = 10 ms^–2)

• A. 25
• B. 50
• C. 100
• D. 18

Answer 1

The Correct Option is B

To determine the number of 100 W lamps that can be lit using the hydroelectric energy generated, we need to follow these steps:

1.  Calculate the gravitational potential energy:
   • Given the height \(h = 40 \, \text{m}\), mass flow rate \(\dot{m} = 9 \times 10^4 \, \text{kg/h}\), and acceleration due to gravity \(g = 10 \, \text{m/s}^2\).
   • Convert the mass flow rate to kg/s: \(\dot{m} = \frac{9 \times 10^4}{3600} \, \text{kg/s} \approx 25 \, \text{kg/s}\).
   • The gravitational potential energy per second is given by: \(P_{\text{gravitational}} = \dot{m} \times g \times h = 25 \times 10 \times 40 = 10000 \, \text{J/s}\).
2. Calculate the electrical energy output:
   • Only 50% of the gravitational potential energy is converted to electrical energy, so \(P_{\text{electrical}} = 0.5 \times 10000 = 5000 \, \text{J/s}\).
3. Determine the number of 100 W lamps:
   • Since power is energy per unit time, and power is measured in watts (1 J/s = 1 W), the electrical power available is \(5000 \, \text{W}\).
   • Each lamp requires \(100 \, \text{W}\), so the number of lamps that can be lit is: \(\frac{5000}{100} = 50\).

Thus, the number of 100 W lamps that can be lit is 50.

Answer 2

The correct answer is (B) : 50 
Total gravitational PE of water per second
\(=\frac{mgh}{T}\)
\(=\frac{9×10^4×10×40}{3600}=10^4\) J/sec
50% of this energy can be converted into electrical energy so total electrical energy
\(=\frac{10^4}{2}=5000 W\)
So total bulbs lit can be
\(=\frac{5000 W}{100 W}\)
= 50 bulbs