The equation of state of some gases can be expressed as `(P+ (a)/(V^(2)))(V-b)= RT`, where P is the pressure, V is the volume, T is the absolute temperature and a, b & R are constants. The dimensions of 'a' are : -

Explanation

By principle of homogeneity of dimensions P can be added to P only. It means `a/V^2` also give pressure.
Dimensional formulae for pressure,
`(P) = M^(-1)L^(-1)T^(-2)`
and volume (V) = `M^0 L^3 T^0`
Since `a/(v^2)` = pressure
`therefore (a)/((M^0 L^3 T^0) = M^1 L^(-1)T^(-2)`
`therefore a = M^1 L^5 T^(-2)`
Similarly, b will have same dimensions as volume . V-b = volume
`therefore b= M^0 L^3 T^0`