A light string passing over a smooth light pulley connects two blocks of masses m₁ and m₂ (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: (b). (m₁ - m₂)/(m₁ + m₂) = 1/8 (taking m₁ as the heavier mass) 8m₁ - 8m₂ = m₁ + m₂ ⇒ 7m₁ = 9m₂ Ratio of masses = 9: 7, so the answer is (b).

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Connected Bodies & Pulleys

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

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Answer: (b)

$\dfrac{m_1 - m_2}{m_1 + m_2} = \dfrac{1}{8}$ (taking $m_1$ as the heavier mass)
$8m_1 - 8m_2 = m_1 + m_2 \Rightarrow 7m_1 = 9m_2$
Ratio of masses $= 9 : 7$ , so the answer is (b).

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