JEE Main Physics: L-Shape Rod COM Shortcut 💡

 

❓ Concept

🎬 Rotational Motion — COM of Bent Rod in 59 Sec

Rod seedhi nahi hai…
right angle pe bent hai?

👉 Samajh jao — COM ko todna padega! 🧠⚙️

Is type ke questions JEE mein frequently aate hain,
aur solution hamesha break–combine method se hota hai 🔥

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🖼️ Concept Image

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✍️ Short Explanation

Centre of mass shape se directly nahi milta —
mass distribution se milta hai.

Isliye bent rod dekhte hi:
👉 use parts mein tod do.

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🔹 Step 1 — Golden Rule of COM (FOUNDATION 💯)**

Centre of mass depends on:

• Mass distribution

• NOT directly on bending or fancy shape

Uniform rod ⇒

$$\text{Mass} \propto \text{Length}$$

📌 Density same ⇒ longer part = heavier part.

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🔹 Step 2 — Bent Rod ⇒ Break Into Parts

Right-angle bent rod ko hamesha:

👉 2 straight rods mein tod do

Har part:

• Uniform

• Known length

• Known orientation (x-axis ya y-axis)

Yahin se problem simple ho jaati hai 😎

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🔹 Step 3 — COM of Each Straight Rod (MOST IMPORTANT 🔥)**

Uniform straight rod ka COM:
👉 Midpoint par hota hai

So:

• Horizontal rod → midpoint on x-axis

• Vertical rod → midpoint on y-axis

📌 Sabse common mistake:
Midpoint galat mark kar dena.

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🔹 Step 4 — System COM Formula

Combined system ke liye:

$$x_{COM}= \frac{m_1x_1+m_2x_2}{m_1+m_2}$$
$$y_{COM}= \frac{m_1y_1+m_2y_2}{m_1+m_2}$$

Since:

$$m \propto L$$

You can directly use:

$$\text{length as mass}$$

👉 No need to calculate actual mass!

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🔹 Step 5 — Vector Form Answer (JEE FAVORITE 🧠)**

Final COM is written as:

$$x_{COM}\,\hat{i} + y_{COM}\,\hat{j}$$

⚠️ Important:

• Direction wrong ⇒ full marks gone

• Origin clearly assume karo (usually corner)

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⭐ Golden Summary Box

• COM depends on mass distribution

• Uniform rod ⇒ mass ∝ length

• Break bent rod into straight parts

• Midpoint of each rod = its COM

• Combine using weighted average

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✅ Final Takeaway

Bent rod ka COM nikalna ho toh:

1️⃣ Rod ko tod do
2️⃣ Har part ka midpoint lo
3️⃣ Length ko mass maan lo
4️⃣ Weighted average laga do

Bas. Question khatam. 🚀