Water is faling on the blades of a turbie at a rate of `300 kg"minute"^(-1)`. The height of the fallsis 200m. The power given the turbine is (Assume `g=10ms^(-2)`)

Options

A. 200kW
B. 100kW
C. 10kW
D. 1kW

Explanation

To find the power given to the turbine by the falling water, we can follow these steps:

### Step 1: Understand the problem
We know that water is falling on the turbine at a rate of 300 kg per minute from a height of 200 m. We need to calculate the power generated by the turbine using the gravitational potential energy of the falling water.

### Step 2: Convert mass flow rate to kg/s
The mass flow rate is given as 300 kg/min. To convert this to kg/s, we divide by 60 (since there are 60 seconds in a minute).

\[ \text{Mass flow rate} (m/T) = \frac{300 \text{ kg}}{60 \text{ s}} = 5 \text{ kg/s} \]

### Step 3: Calculate the gravitational potential energy per second
The gravitational potential energy (GPE) for a mass \( m \) falling from a height \( h \) is given by the formula:

\[ \text{GPE} = mgh \]

Where:
- \( m \) is the mass (in kg)
- \( g \) is the acceleration due to gravity (10 m/s²)
- \( h \) is the height (200 m)

Substituting the values into the equation:

\[ \text{GPE per second} = (5 \text{ kg/s}) \times (10 \text{ m/s}^2) \times (200 \text{ m}) \]

### Step 4: Calculate the power
Now, we can calculate the power \( P \) given to the turbine, which is the rate of work done or energy transferred per unit time:

\[ P = \text{GPE per second} = 5 \times 10 \times 200 \]

Calculating this gives:

\[ P = 10000 \text{ Watts} \]

### Step 5: Convert Watts to Kilowatts
Since power is often expressed in kilowatts (kW), we convert Watts to kilowatts:

\[ P = \frac{10000 \text{ Watts}}{1000} = 10 \text{ kW} \]

### Final Answer
The power given to the turbine is **10 kW**.

---