Examkin

Soru

Zorluk: OrtaFundamental and Derived Units

Match each derived physical quantity in Column I with its equivalent SI unit expressed in terms of fundamental (base) units in Column II.

  • Gravitational Potentialm2⋅s−2\text{m}^2\cdot\text{s}^{-2}
  • Electrical Conductancekg−1⋅m−2⋅s3⋅A2\text{kg}^{-1}\cdot\text{m}^{-2}\cdot\text{s}^3\cdot\text{A}^2
  • Self-Inductancekg⋅m2⋅s−2⋅A−2\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}\cdot\text{A}^{-2}
  • Impulsekg⋅m⋅s−1\text{kg}\cdot\text{m}\cdot\text{s}^{-1}

Cevap

Gravitational Potential matches m2⋅s−2\text{m}^2\cdot\text{s}^{-2}; Electrical Conductance matches kg−1⋅m−2⋅s3⋅A2\text{kg}^{-1}\cdot\text{m}^{-2}\cdot\text{s}^3\cdot\text{A}^2; Self-Inductance matches kg⋅m2⋅s−2⋅A−2\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}\cdot\text{A}^{-2}; Impulse matches kg⋅m⋅s−1\text{kg}\cdot\text{m}\cdot\text{s}^{-1}.
Each derived unit is systematically expressed in terms of the fundamental SI base units (kilogram, meter, second, ampere) by substituting defining formulas. Gravitational potential is energy per unit mass (J⋅kg−1=m2⋅s−2\text{J}\cdot\text{kg}^{-1} = \text{m}^2\cdot\text{s}^{-2}). Electrical conductance is reciprocal resistance (Siemens =A⋅V−1=kg−1⋅m−2⋅s3⋅A2= \text{A}\cdot\text{V}^{-1} = \text{kg}^{-1}\cdot\text{m}^{-2}\cdot\text{s}^3\cdot\text{A}^2). Self-Inductance is electromotive force per rate of change of current (Henry =V⋅s⋅A−1=kg⋅m2⋅s−2⋅A−2= \text{V}\cdot\text{s}\cdot\text{A}^{-1} = \text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}\cdot\text{A}^{-2}). Impulse is force times time (N⋅s=kg⋅m⋅s−1\text{N}\cdot\text{s} = \text{kg}\cdot\text{m}\cdot\text{s}^{-1}).

Adım Adım Çözüm

1
Derive base units for Gravitational Potential
m2⋅s−2\text{m}^2\cdot\text{s}^{-2}
Gravitational potential is potential energy per unit mass (V=Epm=kg⋅m2⋅s−2kgV = \frac{E_p}{m} = \frac{\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}}{\text{kg}}).
2
Derive base units for Electrical Conductance
kg−1⋅m−2⋅s3⋅A2\text{kg}^{-1}\cdot\text{m}^{-2}\cdot\text{s}^3\cdot\text{A}^2
Conductance is current divided by voltage (G=IV=Akg⋅m2⋅s−3⋅A−1G = \frac{I}{V} = \frac{\text{A}}{\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}\cdot\text{A}^{-1}}).
3
Derive base units for Self-Inductance
kg⋅m2⋅s−2⋅A−2\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}\cdot\text{A}^{-2}
Inductance is voltage multiplied by time divided by current (L=V⋅tI=kg⋅m2⋅s−3⋅A−1⋅sAL = \frac{V \cdot t}{I} = \frac{\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}\cdot\text{A}^{-1} \cdot \text{s}}{\text{A}}).
4
Derive base units for Impulse
kg⋅m⋅s−1\text{kg}\cdot\text{m}\cdot\text{s}^{-1}
Impulse is force multiplied by time (I=F⋅t=(kg⋅m⋅s−2)⋅sI = F \cdot t = (\text{kg}\cdot\text{m}\cdot\text{s}^{-2}) \cdot \text{s}).

Anahtar Kavram

Break down derived physical quantities into fundamental SI quantities (mass in kg, length in m, time in s, electric current in A) using defining physical formulas.
Tahmini Süre:1m 30s
Bu soruyu puanla

Konular

Fundamental and Derived Units

Bu konudan daha fazla soru