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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
Of the following quantities, which one has dimensions different from the remaining three
  • A
    Energy per unit volume
  • B
    Force per unit area
  • C
    Product of voltage and charge per unit volume
  • ✓
    Angular momentum per unit mass
✓

Answer

Correct option: D.
Angular momentum per unit mass
d
(d) Energy per unit volume = $\frac{{[M{L^2}{T^{ - 2}}]}}{{[{L^3}]}} = [M{L^{ - 1}}{T^{ - 2}}]$

Force per unit area = $\frac{{[ML{T^{ - 2}}]}}{{[{L^2}]}} = [M{L^{ - 1}}{T^{ - 2}}]$

Product of voltage and charge per unit volume $ = \frac{{V \times Q}}{{{\rm{Volume}}}} = \frac{{VIt}}{{{\rm{Volume}}}} = \frac{{{\rm{Power}} \times {\rm{Time}}}}{{{\rm{Volume}}}}$

$ \Rightarrow $ $\frac{{[M{L^2}{T^{ - 3}}]\,[T]}}{{[{L^3}]}} = [M{L^{ - 1}}{T^{ - 2}}]$

Angular momentum per unit mass = $\frac{{[M{L^2}{T^{ - 1}}]}}{{[M]}} = [{L^2}{T^{ - 1}}]$

So angular momentum per unit mass has different dimension.

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