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JEE MainPhysicsLaws of Motion

Three blocks A, B, and C are connected in series by massless strings and placed on a smooth horizontal table. A horizontal pulling force is applied to block C, causing the entire system to accelerate. The mass of the trailing block A is 2 kg . If the tension in the string connecting blocks B and C is exactly three times the tension in the string connecting blocks A and B, what is the mass of block B?

Options

  1. A6 kg
  2. B4 kg
  3. C2 3 kg
  4. D8 kg

Correct answer

B. 4 kg

Step-by-step solution

Let the common acceleration of the system be a . The tension T₁ in the string between blocks A and B is responsible for accelerating only block A. T₁ = m_A a The tension T₂ in the string between blocks B and C is responsible for accelerating both blocks A and B. T₂ = (m_A + m_B) a Given that T₂ = 3T₁ , we have: (m_A + m_B) a = 3(m_A a) Since a 0 , we can divide by a : m_A + m_B = 3m_A m_B = 2m_A Given m_A = 2 kg , we find: m_B = 2 2 kg = 4 kg Answer: 4 kg

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