KCET 2025 Physics Paper

The problem involves two wires, A and B, made from the same material. The ratio of their diameters is 1:2, and the ratio of their lengths is 1:3. When the same force is applied to both wires, we need to determine the ratio of their length increases.
Here's how we can solve it:
The formula for the increase in length ( ∆ℓ ) when a wire is stretched by a force F is given by:
∆ℓ=‌

Fℓ

AY

=‌

Fℓ

πr2Y

Where:
ℓ is the original length,
A is the cross-sectional area of the wire,
Y is Young's modulus,
r is the radius of the wire.
To find the ratio of the increase in lengths of wires A and B, we calculate:
‌

∆ℓ1

∆ℓ2

=(‌

ℓ1

ℓ2

)×(‌

r2

r1

)2
For wires A and B :
The length ratio ℓ1:ℓ2 is 1:3.
The diameter ratio ( ⇒ radius ratio) is 1:2, so ‌

r2

r1

=‌

2

1

.
Substitute these values into the equation:
‌

∆ℓ1

∆ℓ2

=‌

1

3

×(‌

2

1

)2=‌

1

3

×4=‌

4

3

Therefore, the ratio of the increase in their lengths is 4:3.