A light unstretchable 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:
- 9 : 7
- 4 : 3
- 5 : 3
- 8 : 1
The Correct Option is A
Solution and Explanation
Step 1: Equation for acceleration The acceleration of the system is given by:
\[ a_{\text{sys}} = \frac{(m_2 - m_1)}{m_1 + m_2} \cdot g. \]
Substitute \(a_{\text{sys}} = \frac{g}{8}\):
\[ \frac{(m_2 - m_1)}{m_1 + m_2} \cdot g = \frac{g}{8}. \]
Cancel \(g\) from both sides:
\[ \frac{m_2 - m_1}{m_1 + m_2} = \frac{1}{8}. \]
Step 2: Solve for \(\frac{m_2}{m_1}\) Rearrange the equation:
\[ 8(m_2 - m_1) = m_1 + m_2. \]
Simplify:
\[ 8m_2 - 8m_1 = m_1 + m_2. \]
Combine like terms:
\[ 8m_2 - m_2 = 8m_1 + m_1. \]
\[ 7m_2 = 9m_1. \]
Take the ratio:
\[ \frac{m_2}{m_1} = \frac{9}{7}. \]
Final Answer: \(\frac{m_2}{m_1} = 9 : 7\).
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