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Question

A light string passing over a smooth light pulley connects two block of masses $$m_1$$ and $$m_2$$ (vertically). If the acceleration of the system is $$\left (\dfrac {g}{8}\right )$$, then the ratio of masses is:


A
8:1
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B
9:7
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C
4:3
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D
5:3
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Solution

The correct option is B $$9:7$$
given that $$a = g/8$$
Now FBD for $$m_1$$
$$T -m_1g = m_1 (g/8)$$ ...(1)
and FBD for $$m_2$$
$$m_2g- T = m_2 (g/8)$$ ...(2)
from (1) and (2)
$$g(m_2 - m_1) =\dfrac {g}{8}(m_1 + m_2)$$
$$\Rightarrow 8(m_2- m_1) = m_1 + m_2$$
$$\Rightarrow 8m_2- m_2 = m_1 + 8m_1$$
$$\Rightarrow 7m_2 = 9 m_1$$
$$\Rightarrow \dfrac {m_2}{m_1}=\dfrac {9}{7}$$

256051_280622_ans_f957e8f0fed9409fb48615597719b9bd.png

Physics

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