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Units and Measurement question

2008 · Q146
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Units and Measurement question

2008 · Q146

NEETPhysicsUnits and MeasurementMCQ+4 / −1
Which two of the following five physical parameters have the same dimensions ?
1.  Energy density
2.  Refractive index
3.  Dielectric constant
4.  Young's modulus
5.  Magnetic field
  1. A
    1 and 4
  2. B
    1 and 5
  3. C
    2 and 4
  4. D
    3 and 5
View written solutionFree

Correct answer: A

Energy density = [ML2T−2][L3]=[ML−1T−2]{{\left[ {M{L^2}{T^{ - 2}}} \right]} \over {\left[ {{L^3}} \right]}} = \left[ {M{L^{ - 1}}{T^{ - 2}}} \right][L3][ML2T−2]​=[ML−1T−2]

Young's Modulus(Y) = FA×lΔl{{F \over A} \times {l \over {\Delta l}}}AF​×Δll​

⇒\Rightarrow⇒ [Y] = [MLT−2][L3][L][L]{{\left[ {ML{T^{ - 2}}} \right]} \over {\left[ {{L^3}} \right]}}{{\left[ L \right]} \over {\left[ L \right]}}[L3][MLT−2]​[L][L]​ = [ML−1T−2]\left[ {M{L^{ - 1}}{T^{ - 2}}} \right][ML−1T−2]

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