Question

Find the ratio of \(T_1\) and \(T_2\) for the system shown.

• A. \(\frac{5}{3}\)
• B. \(\frac{3}{5}\)
• C. \(\frac{10}{12}\)
• D. \(\frac{12}{10}\)

Answer 1

The Correct Option is A

Concept: Apply Newton's second law to each mass. Step 1: For mass \(m_1 = 4\,kg\) \[ T_1 - m_1g = m_1 a \] \[ T_1 - 40 = 4a \] \[ T_1 = 40 + 4a \] Step 2: For mass \(m_2 = 4\,kg\) \[ m_2g - T_1 - T_2 = m_2 a \] \[ 40 - T_1 - T_2 = 4a \] Step 3: For mass \(m_3 = 6\,kg\) \[ T_2 - m_3 g = m_3 a \] \[ T_2 - 60 = 6a \] Step 4: Solve Substituting values gives \[ T_1 : T_2 = 5 : 3 \] \[ \frac{T_1}{T_2} = \frac{5}{3} \]