Concept:
Restriction endonucleases are enzymes that recognize specific DNA sequences and cleave DNA at those sites. EcoRI is a Type II restriction enzyme that recognizes the palindromic sequence
\[
5' - GAATTC - 3'
\]
and cuts the DNA to produce sticky ends.
For circular DNA molecules such as plasmids, the number of DNA fragments produced after complete digestion depends on the number of restriction sites.
\[
\boxed{
\text{Number of Fragments}
=
\text{Number of Restriction Sites (Circular DNA)}
}
\]
Step 1: Identify the type of DNA molecule.
The given DNA molecule is a circular plasmid having a size of
\[
6~kb
\]
It contains only one EcoRI recognition site.
Step 2: Understand the effect of digestion.
When EcoRI cuts the plasmid once,
• The circular DNA opens.
• It becomes one linear DNA molecule.
• No additional fragments are produced because there is only one cutting site.
Thus,
\[
\boxed{
1\ \text{Restriction Site}
\Longrightarrow
1\ \text{DNA Fragment}
}
\]
Step 3: Determine the correct option.
Since the plasmid has only one EcoRI site,
\[
\boxed{\text{Number of fragments}=1}
\]
Therefore,
\[
\boxed{Option (B) is correct
\]