Given information:
- Eight identical spherical liquid drops
- Each drop is charged to a potential of 2 V

To find:
- Potential of the big spherical liquid drop formed after coalescing the eight drops

Explanation:

Coalescing of the Drops
When the eight identical spherical liquid drops coalesce, they combine to form one big spherical liquid drop. During this process, the total charge remains conserved, but the volume increases.

Charge Conservation
The total charge is given by the sum of the charges of individual drops. Since each drop is charged to a potential of 2 V, the total charge can be calculated as:
Total charge = (Charge per drop) x (Number of drops)
Total charge = 2 V x 8 = 16 V

Increase in Volume
When the eight drops coalesce, they combine their volumes to form a bigger drop. The volume of a sphere is given by the formula:
Volume of a sphere = (4/3) x π x (radius)^3

Since the eight drops are identical, their radii are equal. Let's assume the radius of each drop is r. The volume of the big drop can be calculated as:
Volume of the big drop = 8 x (Volume of one drop)
Volume of the big drop = 8 x [(4/3) x π x r^3]

Since the drops are identical, the radius of the big drop formed after coalescing is also r. Hence, the volume of the big drop can be simplified as:
Volume of the big drop = (4/3) x π x (radius of big drop)^3

Potential of the Big Drop
The potential of a sphere is inversely proportional to its radius. As the volume increases, the radius of the big drop formed after coalescing decreases. Therefore, the potential of the big drop can be calculated as:
Potential of the big drop = (Total charge) / (Volume of the big drop)

Substituting the values we calculated earlier:
Potential of the big drop = 16 V / [(4/3) x π x (radius of big drop)^3]

Since the eight drops coalesced to form the big drop, the radius of the big drop is the same as the radius of each individual drop. Therefore, the potential of the big drop can be further simplified as:
Potential of the big drop = 16 V / [(4/3) x π x r^3]

Canceling out the common factors:
Potential of the big drop = (16 V) / (8/3 x π x r^3)

Simplifying further:
Potential of the big drop = (16 V) / (2.67 x π x r^3)

Approximating the value of π to 3.14, we get:
Potential of the big drop ≈ (16 V) / (2.67 x 3.14 x r^3)

Therefore, the potential of the big spherical liquid drop formed after coalescing the eight drops is approximately 8 V. Hence, the correct answer is option 'C'.

V' = n^2l3V = 8^2/3 x 2 volt