In a rocket, fuel burns at the rate of 2 kg/s. This fuel gets ejected from the rocket with a velocity of 80 km/s. Force exerted on the rocket is -

Options

A. 16000 N
B. 160000 N
C. 1600 N
D. 16 N

Answer

To find the force exerted on the rocket, we can use the principle of thrust, which is given by the formula:

\[ F = \frac{dm}{dt} \cdot v \]

where:
- \( F \) is the thrust (force) exerted on the rocket,
- \( \frac{dm}{dt} \) is the rate of change of mass (mass flow rate of the fuel),
- \( v \) is the velocity of the ejected fuel.

### Step 1: Identify the given values
- The rate of fuel consumption (\( \frac{dm}{dt} \)) is given as \( 2 \, \text{kg/s} \).
- The velocity of the ejected fuel is given as \( 80 \, \text{km/s} \).

### Step 2: Convert the velocity to meters per second
To use the formula, we need to convert the velocity from kilometers per second to meters per second:

\[ 80 \, \text{km/s} = 80 \times 1000 \, \text{m/s} = 80000 \, \text{m/s} \]

### Step 3: Substitute the values into the thrust formula
Now we can substitute the values into the thrust formula:

\[ F = \frac{dm}{dt} \cdot v = 2 \, \text{kg/s} \cdot 80000 \, \text{m/s} \]

### Step 4: Calculate the force
Now, we perform the multiplication:

\[ F = 2 \cdot 80000 = 160000 \, \text{N} \]

### Step 5: State the final answer
The force exerted on the rocket is:

\[ F = 160000 \, \text{N} \quad \text{(or 160 kN)} \]

### Summary
The force exerted on the rocket is 160,000 Newtons.

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