Two masses of $5 ext{ kg}$ and $10 ext{ kg}$ are connected to a pulley as shown. What will be the accelera

Question

Two masses of $5 	ext{ kg}$ and $10 	ext{ kg}$ are connected to a pulley as shown. What will be the acceleration of the system? ($g$ = acceleration due to gravity)

Accepted Answer

1. **Identify the System:** The problem describes an Atwood Machine, consisting of two masses connected by an inextensible string over a frictionless pulley.
2. **Net Force:** The driving force is the difference in weight between the two masses: $F_{net} = (m_2 - m_1)g$.
3. **Total Mass:** The total mass being accelerated is $M_{total} = m_1 + m_2$.
4. **Calculate Acceleration:** Using Newton's Second Law ($F = ma$):
   $$ a = \frac{F_{net}}{M_{total}} = \frac{m_2 - m_1}{m_2 + m_1}g $$
   Substitute the given values ($m_1 = 5 	ext{ kg}, m_2 = 10 	ext{ kg}$):
   $$ a = \frac{10 - 5}{10 + 5}g = \frac{5}{15}g = \frac{g}{3} $$
   (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion, similar to Exercise 5.16).

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