Question

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. $5 : 3$

Answer 1

Answer: (B)

From F.B.D. of $m_{1} : T-m_{1}g = m_{1} a$ ___ $\left(i\right)$
From F.B.D. of $m_{2} : m_{2}g -T =m_{2} a$ ___ $\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$, $a =\left(\frac{m_{2}-m_{1}}{m_{1}+m_{2}}\right)g$
$\Rightarrow \frac{g}{8}=\left(\frac{m_{2}-m_{1}}{m_{1}+m_{2}}\right)g $
$\Rightarrow \frac{m_{2}}{m_{1}}=\frac{9}{7}$