Question

Two masses \(\mathrm{m_1}\) and \(\mathrm{m_2}\) are attached to a string which passes over a frictionless smooth pulley. When \(\mathrm{m_1} = 10\ \mathrm{kg}\), \(\mathrm{m_2} = 6\ \mathrm{kg}\) the acceleration of masses is

• A. \(20\ \mathrm{m/s^2}\)
• B. \(5\ \mathrm{m/s^2}\)
• C. \(2.5\ \mathrm{m/s^2}\)
• D. \(10\ \mathrm{m/s^2}\)

Hint:

Heavier mass accelerates downward, lighter mass accelerates upward.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For an Atwood machine, acceleration \(a = \frac{(m_1 - m_2)g}{m_1 + m_2}\).
Step 2: Detailed Explanation:
\(a = \frac{10 - 6}{10 + 6} \times 10 = \frac{4}{16} \times 10 = 2.5\ \mathrm{m/s^2}\)
Step 3: Final Answer:
Acceleration is \(2.5\ \mathrm{m/s^2}\).