In 2019, the International Committee for Weights and Measures adopted a new set of denitions for the fundamental units of the SI system. The three important base units in classical mechanics are the unit of time (s), the unit of length (m), and the unit of mass (kg). These three units are derived from three physical constants in the new SI system: Quantity Symbol Units Transition Frequency of Cesium 133 ∆ν s Planck’s Constant h kg ⋅ m2∕s Speed of Light c m∕s Use dimensional analysis to determine the combination of these three parameters that will dene the base units of the SI system. (a) What combination of h, c, and ∆ν denes a second? (b) What combination of h, c, and ∆ν denes a meter? (c) What combination of h, c, and ∆ν denes a kilogram? You only need to nd the combination of h, c, and ∆ν that has the right units. Your answer should not involve any numerical values.
In 2019, the International Committee for Weights and Measures adopted a new set of denitions for the fundamental
units of the SI system. The three important base units in
(m), and the unit of mass (kg). These three units are derived from three physical constants in the new SI system:
Quantity Symbol Units
Transition Frequency of Cesium 133 ∆ν s
Planck’s Constant h kg ⋅ m2∕s
Speed of Light c m∕s
Use dimensional analysis to determine the combination of these three parameters that will dene the base units of
the SI system.
(a) What combination of h, c, and ∆ν denes a second?
(b) What combination of h, c, and ∆ν denes a meter?
(c) What combination of h, c, and ∆ν denes a kilogram?
You only need to nd the combination of h, c, and ∆ν that has the right units. Your answer should not involve any
numerical values.
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