question_answer

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

A) 8 : 1                

B) 9 : 7

C) 4 : 3                

D) 5 : 3

Correct Answer: B

Solution :

[b] From F.B.D. of \[{{m}_{1}}:T-{{m}_{1}}g={{m}_{1}}a\]    (i) From F.B.D. of \[{{m}_{2}}:{{m}_{2}}g-T={{m}_{2}}a\]          (ii) From (i) and (ii), \[a=\left( \frac{{{m}_{2}}-{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}} \right)g\] \[\Rightarrow \frac{g}{8}=\left( \frac{{{m}_{2}}-{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}} \right)g\Rightarrow \frac{{{m}_{2}}}{{{m}_{1}}}=\frac{9}{7}\]