Momentum vs Height Graph – Vertical Motion of Ball | JEE Physics Graphs | Doubtify JEE

 

🏐 Momentum vs Height Graph – Vertical Motion | JEE Physics | Doubtify JEE

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📌 Question:

A ball is thrown vertically upwards (take +z-axis as upwards) from the ground.

👉 Which of the following momentum-height (p–h) graphs correctly represents the motion?

This is a concept-based question that checks your understanding of vector momentum and energy conservation.

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🖼️ Question Image:

🧠 Solution Image:

🧪 Detailed Explanation:

🎯 Motion Summary:

• Ball moves upwards with decreasing speed (positive momentum)

• At the highest point, velocity = 0 ⇒ momentum = 0

• Ball then falls down with increasing speed, but now momentum is negative (since velocity is downward along –z)

🌟 So, what does the p–h graph look like?

Let’s analyze:

1. Momentum (p) is a vector quantity:
   $p = m \cdot v$, direction matters.

2. Height (h) varies from 0 to max height H and then back to 0.

3. As height increases, momentum decreases from +ve to 0

4. As height decreases, momentum goes from 0 to –ve

✅ Final Graph Shape:

A straight line passing through the origin (highest point) with a negative slope:

• Upward motion: +ve momentum

• At top: 0 momentum

• Downward motion: –ve momentum
  ⇒ The graph is a straight line sloping downwards, cutting the h-axis at max height.

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🎥 Video Solution:

🔍 Why This Question is Important:

• Conceptual question from Kinematics & Momentum

• Tests graphical understanding of vector quantities

• Important for assertion-reason and diagram-based MCQs in JEE Mains/Advanced

• Helps in mastering problems involving motion reversal and vector changes

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🧠 Pro Tip:

Always treat momentum as a vector.

• Positive when in direction of axis

• Negative when opposite
  In such questions, draw motion step-by-step and mark velocity signs to get the graph right!

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