CASE 1





The Question is:    d   =   A  +  ( D / C² )    where 'd' is the constant with dimensional formula [ L² ].

So, the dimensions of  ( D / C² )  =  Dimensions of A  =  [ L² ].

Therefore, the dimensions of C²  =  Dimensions of  ( D / A )  =  [ M L ^{- 5} ]

==> Dimensions of C  =  [ M^1/2 L ^{- 5/2} ]

CASE 2





The Question is:    D  =  ( A + d ) / C²    where 'd' is the constant with dimensional formula [ L² ].

So, the dimensions of C²  =  Dimensions of  ( A + d ) / D  =  [ L² ] / [ M L^{- 3} ]  =    [ M ^-1 L⁵ ].

==> Dimensions of C  =  [ M ^-1/2 L^5/2 ]