Physics

Pressure is dimensionally:


ANSWER

Force per unit area

Energy per unit volume

Momentum per unit area per second


SOLUTION
The pressure is defined as the force exerted per unit area.
Pressure $$=\dfrac { Force }{ Area } $$

$$\left[ Pressure \right] =\left[ { ML }^{ -1 }{ T }^{ -2 } \right] $$

$$\Rightarrow \left[ \dfrac { Energy }{ Volume }  \right] =\left[ \dfrac { { ML }^{ 2 }{ T }^{ -2 } }{ { L }^{ 3 } }  \right] =\left[ { ML }^{ -1 }{ T }^{ -2 } \right] $$

$$\Rightarrow \left[ \dfrac { momentum }{ Area\times time }  \right] =\left[ \dfrac { { MLT }^{ -1 } }{ { L }^{ 2 }T }  \right] =\left[ { ML }^{ -1 }{ T }^{ -2 } \right] $$

The dimension of the momentum per unit volume is not the same as that of pressure. So, option $$A,B$$ and $$C$$ are correct.
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