Water is falling on the blades of turbine at a rate of 100 kg/s from a certain spring. IF the height of the spring be 100 m, the power transferred to the turbine will be

Options

A. 100 W
B. 1 kW
C. 10 kW
D. 100 kW

Explanation

To solve the problem of calculating the power transferred to the turbine by the falling water, we can follow these steps:

### Step 1: Understand the formula for power
The power (P) transferred to the turbine can be calculated using the formula:
\[ P = \frac{W}{t} \]
where \( W \) is the work done and \( t \) is the time.

### Step 2: Express work done in terms of force and displacement
The work done (W) can also be expressed as:
\[ W = F \cdot d \]
where \( F \) is the force and \( d \) is the displacement. In this case, the displacement is the height (h) from which the water is falling.

### Step 3: Determine the force acting on the water
The force (F) can be calculated using the formula:
\[ F = m \cdot g \]
where \( m \) is the mass of water and \( g \) is the acceleration due to gravity. Given that the mass flow rate is \( \frac{m}{t} = 100 \, \text{kg/s} \) and taking \( g = 10 \, \text{m/s}^2 \), we can substitute this into the force equation.

### Step 4: Substitute values into the equations
Now we can express the power in terms of the mass flow rate:
\[ P = \frac{m \cdot g \cdot h}{t} \]
Since \( \frac{m}{t} = 100 \, \text{kg/s} \), we can rewrite the equation as:
\[ P = \left(100 \, \text{kg/s}\right) \cdot g \cdot h \]

### Step 5: Plug in the values
Substituting the known values:
- \( g = 10 \, \text{m/s}^2 \)
- \( h = 100 \, \text{m} \)

We have:
\[ P = 100 \, \text{kg/s} \cdot 10 \, \text{m/s}^2 \cdot 100 \, \text{m} \]

### Step 6: Calculate the power
Now, performing the multiplication:
\[ P = 100 \cdot 10 \cdot 100 = 100000 \, \text{W} \]

### Step 7: Convert to kilowatts
Since \( 1 \, \text{kW} = 1000 \, \text{W} \):
\[ P = \frac{100000 \, \text{W}}{1000} = 100 \, \text{kW} \]

### Final Answer
The power transferred to the turbine is **100 kW**.

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