Question

Rocket works on the principle of conservation of :

• A. Mass
• B. Energy
• C. Charge
• D. Momentum

Hint:

Rocket propulsion is a prime example of Newton's Third Law (action-reaction) and the conservation of linear momentum. The rocket pushes gases down (action), and the gases push the rocket up (reaction). The total momentum of the rocket-gas system remains conserved if external forces like air resistance are ignored.

Answer 1

The Correct Option is D

Concept: The operation of a rocket is a classic example of Newton's Third Law of Motion and the principle of conservation of linear momentum. Step 1: Understanding Rocket Propulsion A rocket expels hot gases (burnt fuel) downwards at a very high velocity. According to Newton's Third Law, for every action, there is an equal and opposite reaction. The action is the downward expulsion of gases. The reaction is an upward force (thrust) exerted on the rocket by these gases, which propels the rocket upwards. Step 2: Applying the Principle of Conservation of Linear Momentum The principle of conservation of linear momentum states that if no external forces act on a system, the total linear momentum of the system remains constant. Consider the rocket and its fuel as an isolated system. Initially (before launching or before expelling a particular segment of gas), the rocket and fuel might be at rest or moving with a certain momentum. When the rocket expels a mass of gas (\(m_g\)) downwards with a velocity (\(v_g\)), the gas acquires a downward momentum (\(p_g = m_g v_g\)). To conserve the total momentum of the system (rocket + expelled gas), the rocket itself must gain an equal and opposite momentum. If the rocket has mass \(M_R\) and gains an upward velocity \(V_R\), its upward momentum is \(P_R = M_R V_R\). In a simplified view, if the initial momentum of the system was zero (rocket at rest), then after expelling gas: Total final momentum = Momentum of rocket + Momentum of gas = 0 \(M_R V_R + m_g v_g = 0\) (where \(v_g\) would be negative if \(V_R\) is positive, or vice versa, due to opposite directions). This means \(M_R V_R = -m_g v_g\). The rocket gains momentum in one direction, and the expelled gases gain an equal magnitude of momentum in the opposite direction. Step 3: Evaluating other options
Conservation of Mass (1): While mass is conserved in a non-relativistic sense for the universe, the mass of the rocket itself decreases as it burns and expels fuel. So, it's not the primary principle for its propulsion mechanism in the way momentum conservation is.
Conservation of Energy (2): Energy is also conserved (chemical energy of fuel converts to kinetic energy of rocket and gases, and heat), but the fundamental principle explaining the rocket's motion and change in velocity due to expelled mass is momentum conservation.
Conservation of Charge (3): This principle deals with electric charges and is not directly relevant to the mechanical propulsion of a rocket. The recoil of the rocket due to the ejection of mass is best explained by the conservation of momentum. Therefore, a rocket works on the principle of conservation of momentum.