Dimensions & Dimensional Analysis
1. Give two drawbacks of dimensional analysis?
Solution: Two salient drawbacks of dimensional analysis are:-
i. The method does not tell where the equation is wrong.
ii. If the dimensions had been the same on each side of the equation, we would know only that it might be correct, for the method does not provide a check on numerical factors.
2. What is the importance of dimensional analysis inspite of its drawbacks?
Solution: In many physical situations, it is very difficult to obtain the formula of a physical quantity. It is because the mathematical analysis involved is too difficult. In such situations dimensional analysis can be a powerful tool.
3. What are the basic rules of dimensional analysis?
Solution: There are two simple rules upon which dimensional analysis is based.
i) We can add or subtract quantities only if they have the same dimensions. For example we cannot add an area to a speed to obtain a meaningful sum.
ii) An equation is correct if each and every term on the two sides of an equal sign has the same dimensions. For example in the equation A = B + C, the dimensions of A, B and C must be same.
4. Can dimensional analysis tell you that a physical relation is completely right?
Solution: Even if dimensionally correct, it does not prove that the relation is completely correct. It is because the numerical factors in the relation can be wrong. Thus a dimensional check can tell you when a relation is wrong; it cannot tell you that it is completely right.
5. Why do we use square brackets round M,L and T ?
Solution: We use square brackets round to M,L and T to show that we are dealing with the dimensions of a physical quantity.
6. Can we tell the unit of a physical quantity from its dimensions?
Solution: We can immediately tell the unit of a physical quantity from its dimensions.
7. What is the basic requirement for a physical relation to be correct?
Solution: Dimensional Consistency is the basic requirement for a physical relation to be correct. It is, of course, not sufficient.
8. While deriving the relationships between physical quantities by dimensional analysis, dimensionless constant enters into the relationship. Can you find its magnitude by methods of dimensions?
Solution: We cannot find the magnitude of the dimensionless constant in the relation by the method of dimensions because it is a number. We find its value by experiment or through mathematical investigation.
Dimensional Analysis - Class 11
9. Should an equation describe a physical situation?
Solution: It is very important that every equation must describe some physical situation. An equation can have the correct dimensions in each term without describing any physical situation.
