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 hydroelectric energy number of 100 W lamps, that can be lit, is: (Take g=10ms-2)
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 hydroelectric energy number of 100 W lamps, that can be lit, is: (Take g=10ms-2)
- 25
- 50
- 100
- 18
The Correct Option is B
Solution and Explanation
Total gravitational PE of water per second
=\(\frac{mgh}{T}\)
=\(\frac{9×10^4×10×40}{3600}\)=104 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
\(\therefore ,\) The correct option is (B): 50
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Concepts Used:
Gravitational Potential Energy
The work which a body needs to do, against the force of gravity, in order to bring that body into a particular space is called Gravitational potential energy. The stored is the result of the gravitational attraction of the Earth for the object. The GPE of the massive ball of a demolition machine depends on two variables - the mass of the ball and the height to which it is raised. There is a direct relation between GPE and the mass of an object. More massive objects have greater GPE. Also, there is a direct relation between GPE and the height of an object. The higher that an object is elevated, the greater the GPE. The relationship is expressed in the following manner:
PEgrav = mass x g x height
PEgrav = m x g x h
Where,
m is the mass of the object,
h is the height of the object
g is the gravitational field strength (9.8 N/kg on Earth) - sometimes referred to as the acceleration of gravity.