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)

Updated On: Feb 2, 2026
  • 25
  • 50
  • 100
  • 18
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Approach Solution - 1

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.

Was this answer helpful?
3
2
Hide Solution
collegedunia
Verified By Collegedunia

Approach Solution -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

Was this answer helpful?
0
0

Top Questions on work, energy and power

View More Questions

Concepts Used:

Work, Energy and Power

Work:

  • Work is correlated to force and the displacement over which it acts. When an object is replaced parallel to the force's line of action, it is thought to be doing work. It is a force-driven action that includes movement in the force's direction.
  • The work done by the force is described to be the product of the elements of the force in the direction of the displacement and the magnitude of this displacement.

Energy:

  • A body's energy is its potential to do tasks. Anything that has the capability to work is said to have energy. The unit of energy is the same as the unit of work, i.e., the Joule.
  • There are two types of mechanical energy such as; Kinetic and potential energy.

Read More: Work and Energy

Power:

  • Power is the rate at which energy is transferred, conveyed, or converted or the rate of doing work. Technologically, it is the amount of work done per unit of time. The SI unit of power is Watt (W) which is joules per second (J/s). Sometimes the power of motor vehicles and other machines is demonstrated in terms of Horsepower (hp), which is roughly equal to 745.7 watts.
  • Power is a scalar quantity, which gives us a quantity or amount of energy consumed per unit of time but with no manifestation of direction.