Two bodies of mass $3 ext{ kg}$ and $4 ext{ kg}$ are suspended at the ends of a massless string passing ov

Question

Two bodies of mass $3 	ext{ kg}$ and $4 	ext{ kg}$ are suspended at the ends of a massless string passing over a frictionless pulley. The acceleration of the system is ($g = 9.8 	ext{ m/s}^2$)

Accepted Answer

1. **Analyze the System:** This setup is known as an Atwood machine. Two masses, $m_1 = 3 	ext{ kg}$ and $m_2 = 4 	ext{ kg}$, are connected by a string over a pulley. The heavier mass ($m_2$) accelerates downwards, and the lighter mass ($m_1$) accelerates upwards with the same magnitude $a$.
2. **Apply Newton's Second Law:**
   - For mass $m_1$ (moving up): $T - m_1g = m_1a$
   - For mass $m_2$ (moving down): $m_2g - T = m_2a$
3. **Solve for Acceleration ($a$):**
   Adding the two equations eliminates Tension ($T$):
   $$ m_2g - m_1g = (m_1 + m_2)a $$
   $$ a = g \frac{m_2 - m_1}{m_1 + m_2} $$
4. **Substitute Values:**
   $$ a = 9.8 	imes \frac{4 - 3}{4 + 3} $$
   $$ a = 9.8 	imes \frac{1}{7} $$
   $$ a = 1.4 	ext{ m/s}^2 $$
   (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion, Exercise 5.16 presents a similar problem structure).

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