Question

A rocket motor consumes \(3000\ \text{kg}\) of fuel per minute exhausting it with a speed of \(5\times10^3\ \text{m/s}\). The magnitude of force exerted on rocket is:

• A. \(5\times10^5\ \text{N}\)
• B. \(3\times10^6\ \text{N}\)
• C. \(6\times10^5\ \text{N}\)
• D. \(25\times10^4\ \text{N}\)

Hint:

Rocket thrust is equal to mass ejection rate multiplied by exhaust velocity.

Answer 1

The Correct Option is D

Concept:
The thrust force of a rocket is given by: \[ F=\frac{dm}{dt}v \] where, \[ \frac{dm}{dt}=\text{mass ejected per second} \] and \[ v=\text{exhaust velocity} \]

Step 1: Convert mass consumption per minute into per second. \[ \frac{dm}{dt}=\frac{3000}{60} \] \[ \frac{dm}{dt}=50\ \text{kg/s} \]

Step 2: Write exhaust velocity. \[ v=5\times10^3\ \text{m/s} \]

Step 3: Calculate thrust force. \[ F=50\times 5\times10^3 \] \[ F=250\times10^3 \] \[ F=2.5\times10^5\ \text{N} \] \[ F=25\times10^4\ \text{N} \] \[ \therefore \text{Correct Answer is (D)} \]