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      Question

      Planck’s constant has dimensions equivalent to which

      of the following?
      A Torque Correct Answer Incorrect Answer
      B Linear impulse Correct Answer Incorrect Answer
      C Angular momentum Correct Answer Incorrect Answer
      D Force Ɨ distance² Correct Answer Incorrect Answer

      Solution

      Planck’s constant (denoted as h) has the dimensions of energy Ɨ time, which can also be written as: Energy = [ML²T⁻²] Time = [T] So, h = [ML²T⁻¹] Now, let's compare with the dimensions of other physical quantities: Torque = Force Ɨ distance = [MLT⁻²] [L] = [ML²T⁻²] Linear impulse = Force Ɨ time = [MLT⁻²] [T] = [MLT⁻¹] Angular momentum = Moment of inertia Ɨ angular velocity = [ML²] [T⁻¹] = [ML²T⁻¹] Force Ɨ distance² = [MLT⁻²] [L²] = [ML³T⁻²] Clearly, only angular momentum has the same dimensions as Planck’s constant.

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