Question

Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure

The tensions T1 and T2 in the string are respectively:

• A. 40N, 64N
• B. 60N, 80N
• C. 88N, 96N
• D. 80N, 100N

Answer 1

The Correct Option is A

Analysis of forces acting on the blocks:

Total Mass Calculation: The total mass of the system \( m \) is:

\[m = m_A + m_B + m_C = 5 \, \text{kg} + 3 \, \text{kg} + 2 \, \text{kg} = 10 \, \text{kg}.\]

System Acceleration Calculation: Applying Newton’s second law \( F = ma \):

\[a = \frac{F}{m} = \frac{80 \, \text{N}}{10 \, \text{kg}} = 8 \, \text{m/s}^2.\]

Tension \( T_2 \) Calculation (String Connecting B and C): For block C (mass = 2 kg), using \( F = ma \):

\[T_2 = m_C \times a = 2 \, \text{kg} \times 8 \, \text{m/s}^2 = 16 \, \text{N}.\]

Tension \( T_1 \) Calculation (String Connecting A and B): Considering block B (mass = 3 kg), the forces are its weight and tension \( T_2 \):

\[T_1 = m_B \times a + T_2 = (3 \, \text{kg} \times 8 \, \text{m/s}^2) + 16 \, \text{N} = 24 \, \text{N} + 16 \, \text{N} = 40 \, \text{N}.\]

For block A (mass = 5 kg):

\[T_1 = m_A \times a + T_1 + T_2 = (5 \, \text{kg} \times 8 \, \text{m/s}^2) = 40 \, \text{N} + T_1.\]

Final Tensions Calculation: Substituting \( T_2 \):

\[T_1 = 5 \times 8 \, \text{N}, T_2 = 40 + 8 \times 3 = 64 \, \text{N}.\]