Question

In the pulley-block system shown, the pulley and the block are ideal. If the acceleration of the block is g/8, find m1:m2 (Given m2 > m1)

• A. 7:9
• B. 5:7
• C. 3:4
• D. 9:11

Answer 1

The Correct Option is A

To solve the given problem, let's analyze the forces acting on the blocks and use Newton's second law. Consider the following variables:

• m_1: Mass of block 1
• m_2: Mass of block 2
• g: Acceleration due to gravity
• a = \frac{g}{8}: Acceleration of the blocks
• T: Tension in the string

The forces acting on each block can be described as follows:

1. For block m_1:
   • Weight: m_1 g (downward)
   • Tension: T (upward)
   T - m_1 g = m_1 a
2. For block m_2:
   • Weight: m_2 g (downward)
   • Tension: T (upward)
   m_2 g - T = m_2 a

Add these two equations:

\begin{align*} T - m_1 g &= m_1 a \\ m_2 g - T &= m_2 a \\ \text{Adding both equations:} \\ m_2 g - m_1 g &= m_1 a + m_2 a \\ (m_2 - m_1) g &= (m_1 + m_2) a \\ \end{align*}

Substitute a = \frac{g}{8}:

(m_2 - m_1) g = (m_1 + m_2) \frac{g}{8}

Simplify to find the ratio m_1 : m_2:

\begin{align*} 8(m_2 - m_1) &= m_1 + m_2 \\ 8m_2 - 8m_1 &= m_1 + m_2 \\ 8m_2 - m_2 &= 8m_1 + m_1 \\ 7m_2 &= 9m_1 \\ \frac{m_1}{m_2} &= \frac{7}{9} \end{align*}

Therefore, m_1 : m_2 = 7:9.

The correct answer is 7:9.