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b_q - In physics whenever we have an equality relation both...

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1 In physics, whenever we have an equality relation, both sides of the equation should be of the same type i.e. they must have the same dimensions. For example you cannot have a situation where the quantity on the right-hand side of the equation represents a length and the quantity on the left-hand side represents a time interval. Using this fact, sometimes one can nearly deduce the form of a physical relation without solving the problem analytically. For example if we were asked to find the time it takes for an object to fall from a height of h under the influence of a constant gravitational acceleration g , we could argue that one only needs to build a quantity representing a time interval, using the quantities g and h and the only possible way of doing this is 2 / 1 ) / ( g h a T = . Notice that this solution includes an as yet undetermined coefficient a which is dimensionless and thus cannot be determined, using this method. This coefficient can be a number such as 1 , 2 1 , 3 , π , or any other real number. This method of deducing physical relations is called dimensional analysis . In dimensional analysis the dimensionless coefficients are not important and we do not need to write them. Fortunately in most physical problems these coefficients are of the order of 1 and eliminating them does not change the order of magnitude of the physical quantities. Therefore, by applying the dimensional analysis to the above problem, one obtains 2 / 1 ) / ( g h T = . Generally, the dimensions of a physical quantity are written in terms of the dimensions of four fundamental quantities: M (mass), L (length), T (time), and K (temperature).
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