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Question: Which of the following rations express pressure?...

Which of the following rations express pressure?

A

EnergyVolume\frac{Energy}{Volume}

B

EnergyArea\frac{Energy}{Area}

C

ForceVolume\frac{Force}{Volume}

D

MementumVolume\frac{Mementum}{Volume}

Answer

EnergyVolume\frac{Energy}{Volume}

Explanation

Solution

Pressure =ForceArea=[MLT−2][L2]=[ML−1T−2]= \frac{Force}{Area} = \frac{\lbrack MLT^{- 2}\rbrack}{\lbrack L^{2}\rbrack} = \lbrack ML^{- 1}T^{- 2}\rbrack

 Energy  Volume =[ML2 T−2][L3]=[ML−1 T−2]\frac { \text { Energy } } { \text { Volume } } = \frac { \left[ \mathrm { ML } ^ { 2 } \mathrm {~T} ^ { - 2 } \right] } { \left[ \mathrm { L } ^ { 3 } \right] } = \left[ \mathrm { ML } ^ { - 1 } \mathrm {~T} ^ { - 2 } \right] EnergyVolume=[ML2T−2][L2]=[ML0T−2]\frac{Energy}{Volume} = \frac{\lbrack ML^{2}T^{- 2}\rbrack}{\lbrack L^{2}\rbrack} = \lbrack ML^{0}T^{- 2}\rbrack  Force  Area =[MLT−2][L3]=[ML−2 T−2]\frac { \text { Force } } { \text { Area } } = \frac { \left[ \mathrm { MLT } ^ { - 2 } \right] } { \left[ \mathrm { L } ^ { 3 } \right] } = \left[ \mathrm { ML } ^ { - 2 } \mathrm {~T} ^ { - 2 } \right] MomentumVolume=[MLT−1][L3]=[ML−2T−1]\frac{Momentum}{Volume} = \frac{\lbrack MLT^{- 1}\rbrack}{\lbrack L^{3}\rbrack} = \lbrack ML^{- 2}T^{- 1}\rbrack

Out of the four given ratios only energy/volume express the pressure