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

Answer: (A)

9 : 7

Answer 2

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: $\frac{m_2}{m_1} = 9 : 7$.