Check by the method of dimensions, whether the folllowing relation are dimensionally correct or not. (i) `upsilon = sqrt(P//rho)`, where `upsilon` is velocity. P is prerssure and `rho` is density. (ii) `v= 2pisqrt((I)/(g)),` where I is length, g is acceleration due to gravity and v is frequency.

Answer

(i) correct (ii) correct

Explanation

(i) `upsilon = sqrt(P//rho)`
`LHS = upsilon = [LT^(-1)]`
`RHS = sqrt(p//rho) = sqrt((ML^(-1)T^(-2))/(ML^(-3))) =[LT^(-1)]`
As LHS = RHS, dimensionally, therefore, the
formula is correct.
(ii) `v = 2 pi ((I)/(g))`
`LHS =v = [T^(-1)]`
`RHS = 2pi sqrt((I)/(g)) = sqrt((L)/(LT^(-2))) v= [T]`
As `LHS != RHS,` dimensionally, therefore the
relation is not correct.