A gas satisfies the relation `pV^(5//3) = k`, where p is pressure, V is volume and k is constant. The dimension of constant k are 

Options

A. `[ML^(4)T^(-2)]`
B. `[ML^(2)T^(-2)]`
C. `[ML^(6)T^(-2)]`
D. `[MLT^(-2)]`

Answer

A

Explanation

Given, `pV^(5//3)=k`
Using dimensional balance method
Dimension of `p="ML"^(-1)T^(-2)`
Dimension of `V=L^(3)`
`implies` Dimension of `V^(5//3)=L^(5)`
As, dimension of LHS = Dimension of RHS So, dimension of `k=["ML"^(-1)T^(-2)]xx["L"^(5)]=["ML"^(4)T^(-2)]`