Question

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:

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

Answer 1

The Correct Option is A

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: \(\frac{m_2}{m_1} = 9 : 7\).