In the equation $(P + \frac{a}{v^{2}}) = b \frac{θ}{v}$ , P is pressure, V is volume and $θ$ is absolute temperature. If a and b are constants, the dimension formula of a will be

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${ML}^{- 5} T^{- 1}$

${ML}^{5} T^{- 2}$

${ML}^{5} T^{- 1}$

$M^{- 1} L^{5} T^{2}$

answer is A.

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Detailed Solution

Dimension factor $\frac{a}{v^{2}}$ are same as that of pressure $a = [P] \times [V^{2}]$
$\begin{array}{l} a = [{ML}^{- 1} T^{- 2}] \times {[L^{3}]}^{2} \\ = {ML}^{5} T^{- 2} \end{array}$

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