Wire Elongation Trick: Length vs Diameter in 59 Sec 🔥

 

❓ Concept

🎬 Mechanical Properties of Solids — Wire Elongation Concept in 59 Sec

Same material… same force…
phir bhi ek wire zyada stretch karegi!
👉 Reason length mein hai ya thickness mein? 🤯

Is concept ko pakad liya,
toh ratio-based elasticity questions turant ho jaate hain 🔥

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🖼️ Concept Image

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✍️ Short Explanation

Elasticity ke questions mein formula se zyada dependence matter karta hai.
Yahan ek hi idea kaam karta hai:
👉 Elongation kis cheez par depend karti hai?

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🔹 Step 1 — Elongation Formula (FOUNDATION 💯)**

For a stretched wire:

$$\Delta L=\frac{F\,L}{A\,Y}$$

Where:

• $F$ = applied force

• $L$ = length

• $A$ = cross-sectional area

• $Y$ = Young’s modulus

📌 Core idea: elongation depends on L and A.

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🔹 Step 2 — Same Material ⇒ Same $Y$**

Given: both wires are of the same material.
So:

$$Y_A = Y_B \quad \Rightarrow \quad Y \text{ cancels in ratio}$$

👉 Material ka role zero ho jaata hai (ratio problems mein).

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🔹 Step 3 — Same Force ⇒ $F$ Cancels

Since same force is applied:

$$F_A = F_B \quad \Rightarrow \quad F \text{ cancels}$$

So ab bachta hai:

$$\Delta L \propto \frac{L}{A}$$

📌 Elongation sirf length aur area par depend karegi.

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🔹 Step 4 — Diameter Controls Area (MOST IMPORTANT 🔥)**

Circular wire ke liye:

$$A=\frac{\pi d^2}{4} \quad \Rightarrow \quad A\propto d^2$$

Hence:

$$\boxed{\Delta L \propto \frac{L}{d^2}}$$

🧠 Intuition:

• Longer wire ⇒ more elongation

• Thicker wire ⇒ much less elongation (square effect!)

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🔹 Step 5 — Golden JEE Ratio Rule ⭐

Do wires A aur B ke liye:

$$\boxed{\frac{\Delta L_A}{\Delta L_B} = \frac{L_A}{L_B}\times\frac{d_B^2}{d_A^2}}$$

👉 Bas is ek line se direct ratio mil jaata hai.
No extra steps. No confusion.

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⭐ Golden Summary Box

• Elongation formula: $\Delta L=\frac{FL}{AY}$

• Same material ⇒ $Y$ cancels

• Same force ⇒ $F$ cancels

• Elongation ∝ $L/d^2$
  

• Diameter has stronger effect (square!)

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✅ Final Takeaway

Agar question bole:

“Same material, same force — elongation ratio?”

👉 Turant yaad karo:

$$\boxed{\Delta L \propto \frac{L}{d^2}}$$

Aur ratio rule apply kar do —
JEE mein clean marks 🚀