Force F and density d are related as F = αβ+d then the dimensions of α and β are

The dimensions of left hand side expression should be same as right hand side expression.αβ+d = F =MLT−2The dimensional formula for β should be same as the dimensional formula for dβ = d = ML−312  = M12L−32Hence [α]  = βF = M12L−32MLT−2⇒ α = M32L−12T-2