Solved NEET Physics Problem on Balloon Motion Using Momentum Conservation

Center of Mass & Momentum Explained with NEET-Level Problem

NEET Physics solved problem: An 80 kg man climbs a ladder hanging from a 320 kg hot air balloon. Using conservation of momentum and center of mass principles, we explain the direction and speed of the balloon’s motion step by step. Includes theory, formulas, and exam tips for mastering relative motion and system dynamics. Perfect for NEET aspirants looking for solved exemplar MCQs on mechanics and motion of systems of particles.

🎈 Balloon Physics – NEET Concept: Center of Mass & Momentum

🧩 Question:

An 80 kg man is on a ladder hanging from a balloon that has a total mass of 320 kg (including the basket and passenger). The balloon is initially stationary relative to the ground.

If the man on the ladder begins to climb at 2.5 m/s relative to the ladder:

(a) In what direction does the balloon move?

(b) At what speed does the balloon move?

(c) If the man then stops climbing, what is the speed of the balloon?

🧠 Concept Theory

🔹 Conservation of Momentum

When no external force acts on a system, the total momentum remains constant.

This applies to the man + balloon system because all forces are internal.

Formula:

m₁ × v₁ = m₂ × v₂

Where:

• m₁ = mass of man

• v₁ = velocity of man (relative to ground)

• m₂ = mass of balloon

• v₂ = velocity of balloon

🔹 Center of Mass Principle

In the absence of external forces, the center of mass of the system remains stationary.

So if the man climbs upward, the balloon must move downward to keep the center of mass fixed.

🧮 Step-by-Step Solution

(a) Direction of Balloon’s Motion

The man climbs upward → balloon moves downward.

This is due to conservation of momentum and center of mass stability.

(b) Speed of Balloon

Let:

• mₘₐₙ = 80 kg

• vₘₐₙ = 2.5 m/s (upward)

• m_bₐₗₗₒₒₙ = 320 kg

• v_bₐₗₗₒₒₙ = ? (downward)

Using:

mₘₐₙ × vₘₐₙ = m_bₐₗₗₒₒₙ × v_bₐₗₗₒₒₙ

⇒ 80 × 2.5 = 320 × v_bₐₗₗₒₒₙ

⇒ 200 = 320 × v_bₐₗₗₒₒₙ

⇒ v_bₐₗₗₒₒₙ = 200 ÷ 320 = 0.625 m/s (downward)

(c) When Man Stops Climbing

There’s no internal motion anymore.

So the balloon also stops moving.

Final speed = 0 m/s

📝 Exam Tip

Always check if external forces are present.

If not, use conservation of momentum and center of mass logic.

Relative motion must be converted to ground frame before applying formulas.

🧩 Assertion–Reason Question

Assertion (A):

When a man climbs upward on a ladder hanging from a stationary hot air balloon, the balloon moves downward.

Reason (R):

In the absence of external forces, the center of mass of a system remains stationary relative to the ground.

Options:

(A) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true, but Reason (R) is false.

(D) Assertion (A) is false, but Reason (R) is true.

✅ Correct Answer:

(B) Both Assertion and Reason are true, but Reason is not the correct explanation.

Explanation:

• The balloon moves downward because of conservation of momentum between the man and the balloon.

• The center of mass principle is also true, but it does not directly explain the downward motion in this case. Instead, momentum conservation is the immediate cause.