How much water does a tube-well of 10HP pulls per second . if depth of tube-well is 7.46m(given g=10m/s)?

Options

A. 200kg
B. 100kg
C. 400kg
D. 500kg

Explanation

To determine how much water a tube-well of 10 HP pulls per second when the depth of the tube-well is 7.46 m, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Horsepower to Watts:**
- Given that 1 HP = 746 W, we can convert 10 HP to watts.
\[ \text{Power (P)} = 10 \, \text{HP} \times 746 \, \text{W/HP} = 7460 \, \text{W} \]

2. **Identify the parameters:**
- Depth of the tube-well (h) = 7.46 m
- Acceleration due to gravity (g) = 10 m/s²

3. **Calculate the work done to lift water:**
- The work done (W) to lift a mass (m) of water to a height (h) is given by:
\[ W = mgh \]

4. **Relate power to work done:**
- Power is defined as the work done per unit time (t):
\[ P = \frac{W}{t} \]
- Rearranging gives us:
\[ W = Pt \]

5. **Set the equations equal:**
- From the two equations for work, we have:
\[ Pt = mgh \]

6. **Solve for mass (m):**
- Rearranging gives:
\[ m = \frac{Pt}{gh} \]

7. **Substituting values:**
- Since we want to find out how much water is pulled per second, we can set \( t = 1 \) second.
\[ m = \frac{7460 \, \text{W} \times 1 \, \text{s}}{10 \, \text{m/s}^2 \times 7.46 \, \text{m}} \]

8. **Calculate the mass (m):**
\[ m = \frac{7460}{74.6} \approx 100 \, \text{kg} \]

### Conclusion:
The tube-well pulls approximately **100 kg of water per second**.