Numerical Problems Based on Class 11 Physics Rocket Propulsion

Rocket Propulsion

The propulsion of a rocket is an example of momentum conservation. In a rocket, gases at high temperature and pressure, are produced by the combustion of fuel. They escape with a large constant velocity through a nozzle. The large backward momentum of the gases imparts an equal forward momentum to the rocket. But due to the decrease in the mass of the rocket fuel system, the acceleration of the rocket keeps on increasing.

Burnt out speed of the rocket:

The speed acquired by the rocket when whole of its fuel gets burnt is called the burnt out speed of the rocket.

Thrust on the rocket:

It is the force with which the rocket moves upwards.

Numerical Problems Based on Class 11 Physics Rocket Propulsion with Answers

Q.1. Calculate the ratio m/m₀ for a rocket to attain the escape velocity of 11.2 kms^-1 after starting from rest, when maximum exhaust velocity of the gases is 1.6 kms^-1.

(Ans. 1096)

Q.2. A rocket with a lift mass of 3.5 × 10⁴ kg is blasted up wards with an acceleration of 10 ms^-2. Calculate the initial thrust of the blast.                                            

(Ans. 7.0 × 10⁵ N)

Q.3. Fuel is consumed at the rate of 50 g per second in a rocket. The exhaust gases are rejected at the rate of 5 × 10⁵ cms^-1. What is the thrust experienced by the rocket?

(Ans. 250 N)

Q.4. In the first second of its flight, a rocket ejects 1/60 of its mass with a relative velocity of 2073 ms^-1. What is the initial acceleration of the rocket?

(Ans. 24.75 ms^-2)

Q.5. A rocket motor consumes 100 kg of fuel per second, exhausting it with a speed of 6 × 10³ ms^-1. (i) What thrust is exerted on the rocket? (ii) What will be the velocity of the rocket at the instant its mass is reduced to (1/40)^th of its initial mass, its initial velocity being zero? Neglect gravity.

[Ans. (i) 6 × 10⁵ N (ii) 22.13 × 10³ ms^-1]

Q.6. A balloon of mass m is rising up with an acceleration a. Show that the fraction of weight of the balloon that must be detached in order to double its acceleration is [ma / (2a + g)], assuming the upthrust of air to remain the same.

Q.7. A rocket fired from the earth’s surface ejects 1% of its mass at a speed of 2000 ms^-1 in the first second. Find the average acceleration of the rocket in the first second.

(Ans. 20 ms^-2)

Q.8. A rocket is going upwards with accelerated motion. A man sitting in it feels his weight increased by 5 times his own weight. If the mass of the rocket including that of the man is 1.0 × 10⁴ kg, how much force is being applied by rocket engine? Given g = 10 ms^-2.

(Ans. 5 × 10⁵ N)

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