Dimensional analysis of the relation (Energy)n = (Pressure difference)3/2 (Volume)3/2 gives the value of n as

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Dimensional analysis of the relation (Energy)ⁿ = (Pressure difference)^3/2(Volume)^3/2 gives the value of n as

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1 /2

3 /2

answer is C.

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Detailed Solution

$\begin{array}{l} F^{n} = P^{\frac{3}{2}} V^{\frac{3}{2}} \\ {[{ML}^{2} T^{- 2}]}^{n} = {[{ML}^{- 1} T^{- 2}]}^{\frac{3}{2}} {[L^{3}]}^{\frac{3}{2}} \\ M^{n} L^{2 n} T^{- 2 n} = M^{3 / 2} L^{\frac{- 3}{2} + \frac{9}{2}} T^{- 3} = M^{3 / 2} L^{3} T^{- 3} \\ n = \frac{3}{2} \end{array}$

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