A rocket whose initial mass is 850 kg consumes fuel at the rate of 2.3 kgs^{-1}, The speed of the exhaust gases relative to the rocket engine is 2000 ms^{-1}. What thrust does the rocket engine provide?

This question was previously asked in

HSSC Gram Sachiv Previous Paper 2 (Held on: 9 Jan 2021 Shift 2)

Option 2 : 4600 N

The correct answer is __ 4600 N__.

__ CONCEPT__:

**Rocket**: A rocket works by expelling gases from one end at a very high velocity.- The
**escaping gas has a very high speed**and this with its mass translates to a very large momentum. due to the principle of conservation of momentum the body of the rocket is pushed forward. - The
**propulsion of all rockets**is explained by**Newton's third law of motion**.

- The
- A
**rocket's acceleration depends on three major factor**s:- Exhaust velocity
- Rate the exhaust is ejected
- Mass of the rocket

The **amount of thrust (F _{t}) produced by the engine** is given by:

F_{t }= v × \(\frac{dm}{dt}\)

Where **v is the speed of exhaust gases with respect to rocket** and \(\frac{dm}{dt}\) is **fuel consumption rate** or mass per unit time

The **acceleration (a) of the rocket** is given by:

a = F_{t}/M

Where **M is the mass of the rocket **and F_{t} is the thrust

__ CALCULATION__:

Given that:

M = 850 kg, Fuel consumption rate = \(\frac{dm}{dt}\) = 2.3 kgs-1

Speed of the exhaust gases relative to the rocket engine (v) = 2000 ms-1

**Thrust produced by the engine = Ft = v × \(\frac{dm}{dt}\) = 2000 × 2.3 = 4600 N**

Haryana Patwari/Gram Sachiv 2021: Full Mock Test

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