Answer:
As \[a=\frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}g\] \[\therefore \] \[\frac{g}{8}=\frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}g\] or \[\frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}=\frac{1}{8}\] or \[\frac{({{m}_{1}}+{{m}_{2}})+({{m}_{1}}-{{m}_{2}})}{({{m}_{1}}+{{m}_{2}})-({{m}_{1}}-{{m}_{2}})}=\frac{8+1}{8-1}\] or \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{9}{7}=\mathbf{9:7}\].
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