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Question

The dimensional formula of pressure is

A
$$ [MLT^{-2} ] $$
B
$$ [M^0L^{-1}T^{-2} ] $$
C
$$ [ML^2T^{-2} ] $$
D
$$ [ML^{-1}T^{-2} ] $$
Solution
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Correct option is C. $$ [ML^{-1}T^{-2} ] $$

$$Pressure (P) = \dfrac{Force }{ Area}$$ . . . . . (1)

Since, $$Force = Mass \times Acceleration$$

And, $$Acceleration = \dfrac{Velocity}{Time} =\dfrac{[LT^{-1}]}{[T]}=[LT^{-2}]$$

$$\therefore$$ The dimensional formula of force $$=[M][LT^{-2}]=[MLT^{-2}]$$ . . . . (2)

The dimensional formula of area is $$[M^0L^2T^0]$$ . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

$$Pressure (P) = \dfrac{Force }{ Area}$$

Or,

$$P=\dfrac{[MLT^{-2}]}{[L^2]}=ML^{-1}T^{-2}$$

Therefore, the pressure is dimensionally represented as $$[ML^{-1}T^{-2}]$$

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