A 600 kg rocket is set for vertical firing. If the exhaust speed is 1000m/s, the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is

Options

A. 58.6kg/s
B. 76.4kg/s
C. 6kg/s
D. 117.6kg/s

Explanation

To solve the problem of finding the mass of gas ejected per second (DM/DT) needed to supply the thrust required to overcome the weight of a 600 kg rocket with an exhaust speed of 1000 m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the rocket (m) = 600 kg
- Exhaust speed (v) = 1000 m/s
- Acceleration due to gravity (g) = 10 m/s² (approximately)

2. **Calculate the Weight of the Rocket:**
The weight (W) of the rocket can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 600 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 6000 \, \text{N} \]

3. **Apply the Thrust Equation:**
The thrust (F) produced by the rocket can be expressed in terms of the mass flow rate (DM/DT) and exhaust speed (v):
\[ F = v \cdot \frac{DM}{DT} \]
To maintain vertical firing, the thrust must equal the weight of the rocket:
\[ F = W \]
Therefore, we can set the equations equal to each other:
\[ 6000 \, \text{N} = 1000 \, \text{m/s} \cdot \frac{DM}{DT} \]

4. **Solve for DM/DT:**
Rearranging the equation to find DM/DT:
\[ \frac{DM}{DT} = \frac{6000 \, \text{N}}{1000 \, \text{m/s}} = 6 \, \text{kg/s} \]

5. **Conclusion:**
The mass of gas ejected per second to supply the thrust needed to overcome the weight of the rocket is:
\[ \frac{DM}{DT} = 6 \, \text{kg/s} \]

### Final Answer:
The mass of gas ejected per second is **6 kg/s**.

---