Two bodies of mass $4 ext{ kg}$ and $6 ext{ kg}$ are tied to the ends of a massless string. The string pas

Question

Two bodies of mass $4 	ext{ kg}$ and $6 	ext{ kg}$ are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity ($g$) is:

Accepted Answer

1. **Identify the System:** This setup describes an Atwood Machine, where two masses are suspended over a frictionless pulley via a massless inextensible string.
2. **Forces Involved:** The heavier mass ($m_2 = 6 	ext{ kg}$) accelerates downwards, while the lighter mass ($m_1 = 4 	ext{ kg}$) accelerates upwards. The driving force is the difference in their weights.
3. **Apply Newton's Second Law:**
   $$ a = \frac{	ext{Net Force}}{	ext{Total Mass}} = \frac{(m_2 - m_1)g}{m_1 + m_2} $$
4. **Calculation:** Substitute the given values:
   $$ a = \frac{(6 - 4)g}{6 + 4} = \frac{2g}{10} = \frac{g}{5} $$
   (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion, application of Newton's laws to connected bodies).

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