Question

A light string passing over a smooth light fixed pulley connects two blocks of masses m1 and m2. If the acceleration of the system is g/8, then the ratio of masses is

• A. \(\frac{9}{7}\)
• B. \(\frac{8}{1}\)
• C. \(\frac{4}{3}\)
• D. \(\frac{5}{3}\)

Answer 1

The Correct Option is A

The acceleration \( a \) of the system is given by:

\[ a = \frac{(m_1 - m_2)g}{m_1 + m_2} = \frac{g}{8}. \]

This implies:

\[ 8m_1 - 8m_2 = m_1 + m_2. \]

Rearrange terms:

\[ 7m_1 = 9m_2. \]

Thus, the ratio of \( m_1 \) to \( m_2 \) is:

\[ \frac{m_1}{m_2} = \frac{9}{7}. \]

Therefore, the answer is:

\[ \frac{9}{7}. \]