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(i) The size examines cannot be operated to derive relations other than product of power functions, for example, s = ut + 1/2 at2 or y = y0 cosωt and so on, cannot be derived openly.
(ii) The size examines cannot be operated to measure those relations that involve more than 3 unknowns, Though, we can use them to check the correctness of a relation even if variables are more than 3.
(iii) Even if a physical value relays upon 3 quantities, out of which two have similar dimension then dimensional analysis cannot be applied to derive such a formula but can be used to check the relation.
(iv) Numerical trigonometric ratios, constants and ratios which are dimensionless cannot be derived.
(v) Physical quantities having similar dimensions may not be the similar. For example [ML2T-2] is a dimensional relation for torque as well as work or energy.
Why the work called scalar quantity?
The area element that seems in the integral is a vector. Area like an amount of coverage would appear to be a scalar quantity. What is the way of the area element ? Ans
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application of varignons theorem
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