Question
Planckās constant has dimensions equivalent to which
of the following?Solution
Planckās constant (denoted as h) has the dimensions of energy Ć time, which can also be written as: Energy = [MLĀ²Tā»Ā²] Time = [T] So, h = [MLĀ²Tā»Ā¹] Now, let's compare with the dimensions of other physical quantities: Torque = Force Ć distance = [MLTā»Ā²] [L] = [MLĀ²Tā»Ā²] Linear impulse = Force Ć time = [MLTā»Ā²] [T] = [MLTā»Ā¹] Angular momentum = Moment of inertia Ć angular velocity = [MLĀ²] [Tā»Ā¹] = [MLĀ²Tā»Ā¹] Force Ć distanceĀ² = [MLTā»Ā²] [LĀ²] = [MLĀ³Tā»Ā²] Clearly, only angular momentum has the same dimensions as Planckās constant.
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