A rocket of mass 1000 kg exhausts gases at a rate of 4 kg /sec with a velocity 3000 `m//s` . The thrust developed on the rocket is

Options

A. 12000 N
B. 120 N
C. 800 N
D. 200 N

Answer

To solve the problem of calculating the thrust developed by the rocket, we can follow these steps:

### Step 1: Understand the thrust formula
The thrust (F_th) developed by a rocket can be calculated using the formula:
\[ F_{th} = v_e \times \frac{dm}{dt} \]
where:
- \( v_e \) is the velocity of the exhaust gases,
- \( \frac{dm}{dt} \) is the rate of mass ejection.

### Step 2: Identify the given values
From the problem, we have:
- Mass of the rocket (not directly needed for thrust calculation): \( m = 1000 \, \text{kg} \)
- Rate of mass ejection: \( \frac{dm}{dt} = 4 \, \text{kg/s} \)
- Velocity of exhaust gases: \( v_e = 3000 \, \text{m/s} \)

### Step 3: Substitute the values into the thrust formula
Now, we can substitute the values into the thrust formula:
\[ F_{th} = 3000 \, \text{m/s} \times 4 \, \text{kg/s} \]

### Step 4: Calculate the thrust
Calculating the above expression:
\[ F_{th} = 3000 \times 4 = 12000 \, \text{N} \]

### Step 5: State the final answer
The thrust developed by the rocket is:
\[ F_{th} = 12000 \, \text{N} \]