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Power needed to lift a load or water at a given rate

This type of question, asked 3 times: 28 Jun 2022, 10 Apr 2023, 13 Apr 2023. All 3 questions below, oldest first.

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  1. Question 1

    28 Jun 2022

    95
    Water fall from a 40 m40\text{ }m high dam at the rate of 9×104 kg9 \times10^{4}\text{ }kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W100\text{ }W lamps, that can be lit, is: (Take g=10 ms−2g = 10{\text{ }ms}^{- 2} )

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  2. Question 2

    10 Apr 2023

    119
    If the maximum load carried by an elevator is 1400 kg(600 kg−1400\text{ }kg(600\text{ }kg - Passenger +800 kg+ 800\text{ }kg - elevator), which is moving up with a uniform speed of 3 ms−13{\text{ }ms}^{- 1} and the frictional force acting on it is 2000 NN, then the maximum power used by the motor is_____ kW(g=10 m/s2)kW\left( g = 10\text{ }m/s^{2} \right).

  3. Question 3

    13 Apr 2023

    6
    The ratio of powers of two motors is 3xx+1\frac{3\sqrt{x}}{\sqrt{x}+ 1}, that are capable of raising 300 kg300\text{ }kg water in 5 minutes and 50 kg50\text{ }kg water in 2 minutes respectively from a well of 100 m100\text{ }m deep. The value of xx will be

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