Given:
- The ratio of length, diameter, and specific resistance of two wires is 2:1.
- The resistance of one wire is 10 ohm.

To find:
- The resistance of the other wire.

Explanation:
To solve this problem, we need to understand the relationship between the resistance, length, diameter, and specific resistance of a wire.

1. Resistance:
Resistance is a property of a wire that opposes the flow of electric current. It is denoted by the symbol "R" and measured in ohms (Ω).

2. Length:
The length of a wire is the linear distance between its two ends. It is denoted by the symbol "L" and measured in meters (m).

3. Diameter:
The diameter of a wire is the width of its cross-section. It is denoted by the symbol "d" and measured in meters (m).

4. Specific Resistance:
Specific resistance, also known as resistivity, is a property of a material that determines how strongly it resists the flow of electric current. It is denoted by the symbol "ρ" (rho) and measured in ohm-meters (Ω·m).

The resistance of a wire can be calculated using the formula:

R = (ρ * L) / A

Where:
- R is the resistance of the wire
- ρ is the specific resistance of the material
- L is the length of the wire
- A is the cross-sectional area of the wire

Solution:
Let's assume the resistance of the other wire is "R2".

From the given information, we know that the ratio of length (L1:L2), diameter (d1:d2), and specific resistance (ρ1:ρ2) of the two wires is 2:1.

Let's assign the following values:
- L1 = 2x (length of the first wire)
- L2 = x (length of the second wire)
- d1 = 2y (diameter of the first wire)
- d2 = y (diameter of the second wire)
- ρ1 = 2z (specific resistance of the first wire)
- ρ2 = z (specific resistance of the second wire)

We are given that the resistance of the first wire is 10 ohms, so we can write the equation:

R1 = (ρ1 * L1) / A1 = 10

Substituting the values, we get:

(2z * 2x) / (π * (2y/2)^2) = 10
(4zx) / (π * y^2) = 10

Simplifying the equation, we get:

zx / (π * y^2) = 2.5

Now, let's find the resistance of the second wire (R2) using the same formula:

R2 = (ρ2 * L2) / A2

Substituting the values, we get:

(z * x) / (π * (y/2)^2) = R2

Since we want to find the resistance of the second wire (R2), we need to find the value of (z * x)