Elasticity

Step 1: Formula for Elongation
The amount a wire stretches depends on Young's modulus formula:
Y=‌

Fl

∆lA

=‌

4Fl

∆lπd2

Step 2: What stays the same?
Both wires are made of the same material, have the same length, and the same stretching force. This means their Young's modulus (Y), original length (l), and force (F) are the same.
Step 3: Setting up the equation for both wires
Since Young's modulus is the same for both wires, we set the formulas equal for each wire:
Y1=Y2
‌

4Fl

∆l1πd12

=‌

4Fl

∆l2πd22

Step 4: Rearranging to compare elongations
We can simplify to find how the elongation ( ∆l ) relates to diameter ( d ):
∆l1⋅d12=∆l2⋅d22
So,
∆l2=∆l1⋅(‌

d1

d2

)2
Step 5: Substitute values
We are told ∆l1=1mm (the first wire stretches 1 mm ) and d2=4d1 (the second wire's diameter is 4 times bigger).
∆l2=1⋅(‌

d1

4d1

)2=1⋅(‌

1

4

)2=‌

1

16

mm
Final Answer
The second, thicker wire stretches only ‌

1

16

mm when the same force is applied.