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Question: In the equation \(\left( P + \frac{a}{V^{2}} \right)\) (V-b) = constant, the unit of a is -...

In the equation (P+aV2)\left( P + \frac{a}{V^{2}} \right) (V-b) = constant, the unit of a is -

A

N m5\text{N }\text{m}^{5}

B

N m4\text{N }\text{m}^{4}

C

N m3\text{N }\text{m}^{3}

D

N m2\text{N }\text{m}^{2}

Answer

N m4\text{N }\text{m}^{4}

Explanation

Solution

[a] = [P] [v]2 = ML-1 T -2 L6= MLT -2 L4\lbrack a\rbrack\ = \ \lbrack P\rbrack\ \lbrack v\rbrack^{2}\ = \text{ M}\text{L}^{\text{-1}}\text{ T}\text{ }^{\text{-2}}\text{ }\text{L}^{6} = \text{ MLT}\text{ }^{\text{-2}}\text{ }\text{L}^{4}

\ unit = Nm4