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NEET PHYSICSEasy

Two masses of 5 kg5 \text{ kg} and 10 kg10 \text{ kg} are connected to a pulley as shown. What will be the acceleration of the system? (gg = acceleration due to gravity)

A

gg

B

g2\frac{g}{2}

C

g3\frac{g}{3}

D

g4\frac{g}{4}

Step-by-Step Solution

  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: Fnet=(m2−m1)gF_{net} = (m_2 - m_1)g.
  3. Total Mass: The total mass being accelerated is Mtotal=m1+m2M_{total} = m_1 + m_2.
  4. Calculate Acceleration: Using Newton's Second Law (F=maF = ma): a=FnetMtotal=m2−m1m2+m1ga = \frac{F_{net}}{M_{total}} = \frac{m_2 - m_1}{m_2 + m_1}g Substitute the given values (m1=5 kg,m2=10 kgm_1 = 5 \text{ kg}, m_2 = 10 \text{ kg}): a=10−510+5g=515g=g3a = \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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