To find the ratio of electrical resistance of the three wires made of copper, we will follow these steps:
### Step 1: Understand the formula for electrical resistance
The electrical resistance \( R \) of a wire is given by the formula:
\[
R = \frac{\rho L}{A}
\]
where:
- \( R \) = resistance
- \( \rho \) = resistivity of the material (constant for copper)
- \( L \) = length of the wire
- \( A \) = cross-sectional area of the wire
### Step 2: Relate mass, volume, and density
The volume \( V \) of the wire can be expressed as:
\[
V = A \times L
\]
Also, the volume can be related to mass \( M \) and density \( D \) as:
\[
V = \frac{M}{D}
\]
Thus, we can equate the two expressions for volume:
\[
A \times L = \frac{M}{D}
\]
From this, we can express the cross-sectional area \( A \) as:
\[
A = \frac{M}{D \times L}
\]
### Step 3: Substitute \( A \) in the resistance formula
Substituting the expression for \( A \) into the resistance formula:
\[
R = \frac{\rho L}{\frac{M}{D \times L}} = \frac{\rho L^2 D}{M}
\]
### Step 4: Find the ratios of resistance
Now, we need to find the ratio of resistances \( R_1 : R_2 : R_3 \) for the three wires. The mass ratios are given as \( 1 : 3 : 5 \) and the length ratios as \( 5 : 3 : 1 \).
Let:
- \( M_1 = 1 \), \( M_2 = 3 \), \( M_3 = 5 \)
- \( L_1 = 5 \), \( L_2 = 3 \), \( L_3 = 1 \)
Using the formula for resistance:
\[
R_1 = \frac{\rho L_1^2 D}{M_1}, \quad R_2 = \frac{\rho L_2^2 D}{M_2}, \quad R_3 = \frac{\rho L_3^2 D}{M_3}
\]
### Step 5: Calculate \( R_1, R_2, R_3 \)
Substituting the values:
\[
R_1 = \frac{\rho (5^2) D}{1} = 25\rho D
\]
\[
R_2 = \frac{\rho (3^2) D}{3} = \frac{9\rho D}{3} = 3\rho D
\]
\[
R_3 = \frac{\rho (1^2) D}{5} = \frac{\rho D}{5}
\]
### Step 6: Form the ratio \( R_1 : R_2 : R_3 \)
Now, we can express the ratio:
\[
R_1 : R_2 : R_3 = 25\rho D : 3\rho D : \frac{\rho D}{5}
\]
To simplify, we can factor out \( \rho D \):
\[
= 25 : 3 : \frac{1}{5}
\]
### Step 7: Eliminate the fraction
To eliminate the fraction, multiply all parts of the ratio by 5:
\[
= 25 \times 5 : 3 \times 5 : 1 = 125 : 15 : 1
\]
### Final Answer
Thus, the ratio of their electrical resistance is:
\[
\boxed{125 : 15 : 1}
\]
