Question

The equations (p+a/v²)(v-b)=constant find the dimensions of a and b.
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Answer 1

Explanation:

We can add and structure only like quantities.

⇒ Dimensions of P = Dimensions of

V^2a ...... (i)

and dimension of V = Dimensions of b ............ (ii)

From (i),

Dimensions of a = Dimensions of P× Dimensions of V^2

2[a]=[M 1 L −1 T −2 ]×[L 3 ] 2

=[M 1 L 5 T −2]

Unit of a= Unit of p×Unit of v = m 2N×m 6=Nm 4

From (ii), [b] = [V]=[M 0 L 3 T 0]So unit of b = Unit of V = m^3

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