$A$ plasmid $DNA$ and a linear $DNA$ (both are of the same size) have one site for a restriction endonuclease. When cut and separated on agarose gel electrophoresis,the plasmid shows one $DNA$ band while the linear $DNA$ shows two fragments. Explain.

(N/A) The reason for this observation is the structural difference between the two $DNA$ molecules:
$1$. $A$ plasmid is a circular $DNA$ molecule. When it is cut with a restriction enzyme at a single site,it becomes linearized but remains a single continuous molecule. Therefore,it appears as a single band on the agarose gel.
$2$. $A$ linear $DNA$ molecule,when cut at a single site,is cleaved into two separate fragments. Since these fragments have different sizes,they appear as two distinct bands on the agarose gel.
Thus,the circular nature of the plasmid prevents fragmentation upon a single cut,whereas the linear $DNA$ is physically separated into two pieces.