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  4. A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the blocks is g/8 , then the ratio of the masses is :

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Q. 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 blocks is $g/8$ , then the ratio of the masses is :

NTA AbhyasNTA Abhyas 2020

Solution:

$FBD$ of system
Solution
Considering $m_{2}>m_{1}$
$m_{2}g-T=m_{2}a...\left(i\right)$
$T-m_{1}g=m_{1}a...\left(ii\right)$
$a=\frac{\left(m_{2} - m_{1}\right)}{m_{1} + m_{2}}g$
Given, $a=g/8\Rightarrow \frac{g}{8}=\left(\frac{m_{2} - m_{1}}{ m_{1} + m_{2}}\right)g$
$m_{1}+m_{2}=8\left(m_{2} - m_{1}\right)$
$7m_{2}=9m_{1}$
$\frac{m_{2}}{ m_{1}}=\frac{9}{7}$