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      Question

      A block of mass 10 kg is on a horizontal table with

      friction coefficient μ = 0.2. A mass of 4 kg is suspended from a frictionless pulley attached to this block. Find the acceleration of the system. (g = 10 m/s²)
      A 1.43 m/s² Correct Answer Incorrect Answer
      B 2.0 m/s² Correct Answer Incorrect Answer
      C 2.86 m/s² Correct Answer Incorrect Answer
      D 3.33 m/s² Correct Answer Incorrect Answer

      Solution

      • Mass of block on table: M = 10 kg
      • Coefficient of friction: μ = 0.2
      • Suspended mass: m = 4 kg
      • Gravitational acceleration: g = 10 m/s²
      • Pulley is frictionless, and the string is light and inextensible
      System Setup:
      • The 10 kg block is on the table and connected to the 4 kg hanging mass via a pulley.
      • Let the entire system move with acceleration a.
      • Let the tension in the string be T.
      Forces on the 4 kg hanging mass (m)
      • Downward force: m·g = 4 × 10 = 40 N
      • Upward tension: T
      • Equation of motion:
        m·g – T = m·a
        ⇒ 40 – T = 4a → (1)
      Forces on the 10 kg block (M)
      • Horizontal tension pulling right: T
      • Friction opposes motion: f = μ·M·g = 0.2 × 10 × 10 = 20 N
      • Net force: T – f = M·a
        ⇒ T – 20 = 10a → (2)
      Solve equations (1) and (2) From (1):
      T = 40 – 4a Substitute into (2): (40 – 4a) – 20 = 10a
      ⇒ 20 – 4a = 10a
      ⇒ 20 = 14a
      ⇒ a = 20 / 14 = 10 / 7 ≈ 1.43 m/s² Therefore, the correct answer is option (a).

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