Why dimensional methods are applicable only up to three quantities?

Why dimensional methods are applicable only up to three quantities? Because on equating the powers of M,L and T on either side of the dimensional equation, three equations can be obtained, from which only three unknown dimensions can be calculated.

What are the limitations of dimensional analysis?

Dimensional Analysis can’t derive relation or formula if a physical quantity depends upon more than three factors having dimensions. It can’t derive a formula containing trigonometric function, exponential function, and logarithmic function and it can’t derive a relation having more than one part in an equation.

Can two or more than two quantities have the same dimensions?

1) two physical quantities can only be equated if they have the same dimensions 2) two physical quantities can only be added if they have the same dimensions 3) the dimensions of the multiplication of two quantities is given by the multiplication of the dimensions of the two quantities.

Why it is not possible to establish a physical relation involving more than three variable using the method of dimensions?

Answer: It cannot be used if the physical quantity is dependent on more than three unknown variables. This method cannot be used if the physical quantity contains more than one term, say sum or difference of two terms i.e it does not always tell us the exact form of a relation.

What are two limitations of dimensional analysis?

What are the limitations of dimensional analysis? The limitations of dimensional analysis are: (i) We cannot derive the formulae involving trigonometric functions, exponential functions, log functions etc., which have no dimension. (ii) It does not give us any information about the dimensional constants in the formula.

Which is not a limitation of dimensional analysis?

The method cannot be considered to derive composite relations. A formula containing trigonometric function, exponential function, and logarithmic function can not derive from it. The method cannot be used to derive the relationship between more than three quantities.

Can dimensions be added?

We can add or multiply two quantities of different dimensions by converting one quantity in terms of the dimension of the other quantity. Example 1: Combined length of two cords of 1m and 50 cm = (1*100)cm + 50 cm = 150 cm.

What are the limitations and applications of dimensional analysis?

Limitations of Dimensional Analysis It doesn’t give information about the dimensional constant. The formula containing trigonometric function, exponential functions, logarithmic function, etc. cannot be derived. It gives no information about whether a physical quantity is a scalar or vector.