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Zorluk: KolayDimensions of Physical Quantities and Dimensional Analysis

Power is defined as the rate at which work is done or energy is transferred. Which of the following expressions represents the correct dimensional formula for power?

  1. ML2T−3M L^2 T^{-3}Cevap
  2. B
    ML2T−2M L^2 T^{-2}
  3. C
    MLT−3M L T^{-3}
  4. D
    MLT−2M L T^{-2}

Cevap

ML2T−3M L^2 T^{-3}
Power is defined as work done per unit time (P=WtP = \frac{W}{t}). The dimensional formula for work is [W]=ML2T−2[W] = M L^2 T^{-2}, and for time is [t]=T[t] = T. Dividing work by time gives [P]=ML2T−2T=ML2T−3[P] = \frac{M L^2 T^{-2}}{T} = M L^2 T^{-3}.

Adım Adım Çözüm

1
Write the fundamental definition of power in terms of work and time.
Power=WorkTime\text{Power} = \frac{\text{Work}}{\text{Time}}
By definition, power measures the rate of doing work.
2
Determine the dimensions of work.
[Work]=[Force]×[Distance]=(MLT−2)×L=ML2T−2[\text{Work}] = [\text{Force}] \times [\text{Distance}] = (M L T^{-2}) \times L = M L^2 T^{-2}
Force has dimensions of mass times acceleration (MLT−2M L T^{-2}), and multiplying by distance (LL) yields energy or work dimensions.
3
Divide the dimensions of work by the dimension of time (TT).
[Power]=ML2T−2T=ML2T−3[\text{Power}] = \frac{M L^2 T^{-2}}{T} = M L^2 T^{-3}
Dividing by time increases the negative exponent of time from −2-2 to −3-3.

Anahtar Kavram

Dimensional Formula for Power
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Dimensions of Physical Quantities and Dimensional Analysis

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