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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 × distance² Correct Answer Incorrect Answer

    Solution

    Planck’s constant (denoted as h) has the dimensions of energy × 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 × distance = [MLT⁻²] [L] = [ML²T⁻²] Linear impulse = Force × time = [MLT⁻²] [T] = [MLT⁻¹] Angular momentum = Moment of inertia × angular velocity = [ML²] [T⁻¹] = [ML²T⁻¹] Force × distance² = [MLT⁻²] [L²] = [ML³T⁻²] Clearly, only angular momentum has the same dimensions as Planck’s constant.

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