MCQ
The unit $J \,P{a^{ - 1}}$ is equivalent to
  • ${m^3}$
  • B
    $c{m^3}$
  • C
    $d{m^3}$
  • D
    None of these

Answer

Correct option: A.
${m^3}$
a
(a) $J \,P{a^{ - 1}}$; Unit of work is Joule and unit of pressure is Pascal.

Dimension of Joule i.e. work $ = F \times L$ $ = ML{T^{ - 2}} \times L$

$ = \left[ {M{L^2}{T^{ - 2}}} \right]$

$\frac{1}{{Pa}} = \frac{1}{{{\rm{Pressure}}}} = \frac{1}{{\frac{F}{A}}} = \frac{{1 \times A}}{F} = \left[ {ML{T^{ - 1}}} \right]$

So, $J \,P{a^{ - 1}}$ $ = \left[ {M{L^2}{T^2}} \right]$ $ = \left[ {{L^2} \times L} \right]\; = \left[ {{L^3}} \right]$.

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