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

Answer: (A)

$\frac{9}{7}$

Answer 2

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:

$\frac{9}{7}.$