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Units and Measurements question

2020 · 3 Sep · Shift 2 · Q53
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Units and Measurements question

2020 · 3 Sep · Shift 2 · Q53

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar constant. Dimension of solar constant is :
  1. A
    MLT–2
  2. B
    ML0T–3
  3. C
    M2L0T–1
  4. D
    ML2T–2
View written solutionFree

Correct answer: B

  1. Interpret the physical quantity

The solar constant is defined as the solar energy received per unit area per unit time.

So,

Solar constant=EnergyArea×Time\text{Solar constant} = \frac{\text{Energy}}{\text{Area} \times \text{Time}}Solar constant=Area×TimeEnergy​
  1. Write dimensions of each quantity
  • Energy has dimensions:
[E]=ML2T−2[E] = ML^2T^{-2}[E]=ML2T−2
  • Area has dimensions:
[A]=L2[A] = L^2[A]=L2
  • Time has dimensions:
[T]=T[T] = T[T]=T
  1. Find dimensions of solar constant
[Solar constant]=ML2T−2L2⋅T[\text{Solar constant}] = \frac{ML^2T^{-2}}{L^2 \cdot T}[Solar constant]=L2⋅TML2T−2​ =ML2−2T−2−1= M L^{2-2} T^{-2-1}=ML2−2T−2−1 =ML0T−3= ML^0T^{-3}=ML0T−3
  1. Match with the options

The correct dimension is:

ML0T−3ML^0T^{-3}ML0T−3

So the correct option is B.

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