Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

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

$4.9 \text{ m/s}^2$

$2.45 \text{ m/s}^2$

$1.4 \text{ m/s}^2$

$9.5 \text{ m/s}^2$

Step-by-Step Solution

Analyze the System: This setup is known as an Atwood machine. Two masses, $m_1 = 3 \text{ kg}$ and $m_2 = 4 \text{ kg}$ , 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 $a$ .
Apply Newton's Second Law:

For mass $m_1$ (moving up): $T - m_1g = m_1a$
For mass $m_2$ (moving down): $m_2g - T = m_2a$

Solve for Acceleration ( $a$ ): Adding the two equations eliminates Tension ( $T$ ): $m_2g - m_1g = (m_1 + m_2)a$ $a = g \frac{m_2 - m_1}{m_1 + m_2}$
Substitute Values: $a = 9.8 \times \frac{4 - 3}{4 + 3}$ $a = 9.8 \times \frac{1}{7}$ $a = 1.4 \text{ m/s}^2$ (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion, Exercise 5.16 presents a similar problem structure).

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