question_answer

A light string passing over a smooth pulley connects two blocks of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] (vertically). If the acceleration of the system is \[g/8,\]find the ratio of the two masses.               

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            \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{9}{7}=\mathbf{9:7}\].