​The resistivity of the material of wire having resistance 0.7Ω0.7Ω​, length 1 m and diameter 0.2 mm is:​​

Correct option is A

​​The correct answer is(A) ​2.2×10−8Ωm​​.

To find the electrical resistivity of the material of the wire, we can use the formula for resistance:

$$R=\frac{ρL}{A}$$​

Where:
- R is the resistance (in ohms),
- ρ is the resistivity (in ohm-meters),
- L is the length of the wire (in meters),
- A is the cross-sectional area of the wire (in square meters).

Step 1: Convert Length and Diameter to Appropriate Units
The length of the wire is given as 100 cm, which we need to convert to meters:
$$L=100cm=1m$$​

The diameter of the wire is given as 0.2 mm, which we also need to convert to meters:$${Diameter}={2.0mm}={2.0}\times{10}^{-4}m$$​

Step 2: Calculate the Radius
The radius r is half of the diameter:$$r=\frac{Diameter}{2}=\frac{{2.0}\times{10}^{−4}}{2}={1.0}\times{10}^{−4}m$$​

Step 3: Calculate the Cross-Sectional Area
The cross-sectional area A of the wire can be calculated using the formula for the area of a circle:
A=πr2
Substituting the radius:$$A={π} {({1.0}\times{10}^{−4})}^{2}={π} {1.0}×{10}^{−8}$$​

Using π≈3.14:$$A≈{3.14}×{10}^{−8}{m}^2$$​

Step 4: Rearranging the Resistance Formula
We need to find the resistivity ρ. Rearranging the formula gives us:
$$ρ=\frac{R⋅A}L$$​

Step 5: Substitute the Known Values
Now we can substitute the known values into the equation. The resistance R is given as 0.7 ohms:$$ρ=\frac{{0.7}⋅ {(3.14}\times{10}^{−8)}}{1}$$​

Step 6: Calculate the Resistivity
Calculating the above expression:$$ρ≈{0.7}\times{3.14}\times{10}^{−8}$$​
$$ρ≈{2.198}\times{10}^{−8}{ohmmeters}$$$$ρ≈{2.198}\times{10}^ {−8}ohmmeters$$​

Final Answer
Thus, the electrical resistivity of the material is approximately:$$ρ≈{2.2}\times{10}^{−8}ohmmeters$$​