The meselson-stahl experiments and this paper are considered important, groundbreaking studies in molecular biology. some of the clarity of the centrifugation results was due to the fact that the dna was fragmented during handling (although the experimenters did not know it at the time.) when dna breaks into fragments, the sugar-phosphate backbone is broken forming many short double helices. why did the fragmented dna still show the same pattern of nitrogen density banding?

Fragmentation of a larger DNA molecule into many smaller pieces occurs by breaking some of the phosphodiester bonds and does not affect the density of the N14 and N15 atoms in the nucleotides which in turn was the basis of nitrogen density banding.

Explanation:

Meselson and Stahl experiment proved the semi-conservative nature of DNA replication based on the banding pattern obtained in CsCl density gradient centrifugation.  

They grew the E coli cells in the N15 medium for one generation and transferred them to the N14 medium. The presence of N15 and N14 isotopes in deoxyribonucleotides were measured by the banding pattern obtained in CsCl density gradient centrifugation.  

Breaking the DNA molecule into smaller double helices occurs when the phosphodiester bonds between two consecutive nucleotides are broken. The total amount of N14 and N15 atoms in the nucleotides in an intact DNA is equal to that of the nucleotides present in all the smaller pieces of the DNA. Therefore breaking down the DNA did not affect the density pattern obtained in the centrifugation.