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NEET PHYSICSLAWS OF MOTIONEasy

Question

Two bodies of mass 3 kg3 \text{ kg} and 4 kg4 \text{ kg} are suspended at the ends of a massless string passing over a frictionless pulley. The acceleration of the system is (g=9.8 m/s2g = 9.8 \text{ m/s}^2)

A

4.9 m/s24.9 \text{ m/s}^2

B

2.45 m/s22.45 \text{ m/s}^2

C

1.4 m/s21.4 \text{ m/s}^2

D

9.5 m/s29.5 \text{ m/s}^2

Step-by-Step Solution

  1. Analyze the System: This setup is known as an Atwood machine. Two masses, m1=3 kgm_1 = 3 \text{ kg} and m2=4 kgm_2 = 4 \text{ kg}, are connected by a string over a pulley. The heavier mass (m2m_2) accelerates downwards, and the lighter mass (m1m_1) accelerates upwards with the same magnitude aa.
  2. Apply Newton's Second Law:
  • For mass m1m_1 (moving up): Tm1g=m1aT - m_1g = m_1a
  • For mass m2m_2 (moving down): m2gT=m2am_2g - T = m_2a
  1. Solve for Acceleration (aa): Adding the two equations eliminates Tension (TT): m2gm1g=(m1+m2)am_2g - m_1g = (m_1 + m_2)a a=gm2m1m1+m2a = g \frac{m_2 - m_1}{m_1 + m_2}
  2. Substitute Values: a=9.8×434+3a = 9.8 \times \frac{4 - 3}{4 + 3} a=9.8×17a = 9.8 \times \frac{1}{7} a=1.4 m/s2a = 1.4 \text{ m/s}^2 (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion, Exercise 5.16 presents a similar problem structure).

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from LAWS OF MOTION. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSLAWS OF MOTIONbodiessuspendedmasslessstringpassing

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