A light stretchable string passing over a smooth light pulley connects two blocks of masses and . If the acceleration of the system is, then the ratio of the masses is:

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Solution

Q.
A light stretchable string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ . If the acceleration of the system is $\frac{g}{8}$ , then the ratio of the masses $\frac{m_{2}}{m_{1}}$ is: [2024]

1 9 : 7

2 4 : 3

3 5 : 3

4 8 : 1

Ans.
(1)

$a_{c} = \frac{(m_{2} - m_{1}) g}{(m_{1} + m_{2})} \Rightarrow \frac{g}{8} = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g$

$\frac{1}{8} = (\frac{\frac{m_{2}}{m_{1}} - 1}{\frac{m_{2}}{m_{1}} + 1}) \Rightarrow \frac{m_{2}}{m_{1}} + 1 = 8 \frac{m_{2}}{m_{1}} - 8 \Rightarrow \frac{m_{2}}{m_{1}} = \frac{9}{7}$

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