A particle of mass m is located in a region where its potential energy `[U(x)]` depends on the position x as potential Energy `[U(x)]=(a)/(x^2)-(b)/(x)` here a and b are positive constants…
(i) Write dimensional formula of a and b
(ii) If the time perios of oscillation which is calculated from above formula is stated by a student as `T=4piasqrt((ma)/(b^2))`, Check whether his answer is dimensionally correct.

Explanation

(i) `[a]=[Ux^(2)]=ML^(2)T^(-2)L^(2)=[ML^(4)T^(-2)], [b]=[Ux]=ML^(2)T^(-2)L=[ML^(3)T^(-2)]`
(ii) `T=4 pi a sqrt((ma)/b^(2))=4 pisqrt((ma^(3))/b^(2))`, Dimension of `RHS=[4pisqrt((ma^(3))/b^(2))]=sqrt((MM^(3)L^(12)T^(-6))/(M^(2)L^(6)T^(-4))) ne T`
So, his answer is dimensionally incorrect