A patient is scanned by two separate magnetic resonance imaging machines. One is a conventional $1$ Tesla device configured to image $1$H nuclei, while the other is a $5$ Tesla research scanner which images $13$C nuclei. Assuming that the number density of hydrogen nuclei relative to carbon nuclei in the body is $10$ and the isotopic abundance of $13$C is $1\%,$ estimate the ratio between the MRI signal strengths obtained in the two scanners. The gyromagnetic ratios of $1$H and $13$C are $2\mathrm{.}68$times $108$

rads$/$s$/$T and $6\mathrm{.}72$times $107$

rads$/$s$/$T respectively.