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Question: The unit J \(Pa^{- 1}\)is equivalent to...

The unit J Pa−1Pa^{- 1}is equivalent to

A

m3m^{3}

B

cm3cm^{3}

C

dm3dm^{3}

D

None of these

Answer

m3m^{3}

Explanation

Solution

JPa­­–1; Unit of work is Joule and unit of pressure is Pascal.

Dimension of Joule i.e. work =F×L= F \times L =MLT−2×L= MLT^{- 2} \times L

=[ML2T−2]= \left\lbrack ML^{2}T^{- 2} \right\rbrack

1Pa=1Pressure=1FA=1×AF=[MLT−1]\frac{1}{Pa} = \frac{1}{\text{Pressure}} = \frac{1}{\frac{F}{A}} = \frac{1 \times A}{F} = \left\lbrack MLT^{- 1} \right\rbrack

So, JPa–1=[ML2T2]=[L2×L] 6mu=[L3]= \left\lbrack ML^{2}T^{2} \right\rbrack = \left\lbrack L^{2} \times L \right\rbrack\mspace{6mu} = \left\lbrack L^{3} \right\rbrack.