) = sin( ) = wrong, sine function must be dimensionless. RHS = sin( ) = sin() = wrong, since trigonometric function must be dimension less. Trigonometric function sine is a ratio, hence it must be dimensionless.ĭimensions of RHS = sin(. Rule out the wrong formulas on dimensional grounds.ĭimension of a = displacement = ĭimension of v (speed) = distance/time = ĭimension of t or T (time period) = (a = maximum displacement of the particle, v = speed of the particle. Q9 (NCERT): A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion: To check the dimensional correctness of a given equation.establish a relationship between different physical quantities in an equation. To convert a physical quantity from one system of units to another. Q8: What are the uses (applications) of dimensional analysis?Īnswer: The applications of dimensional analysis are:
In equation X + Y = Z is valid if the dimensions of X, Y and Z are same.Īnswer: Fourier (Joseph Fourier – French Mathematician) This principle is based on the fact that two quantities of the same dimension only can be added up, and the resulting quantity also possess the the same dimension. On What principle is it based?Īnswer: The principle of homogeneity of dimensions states that an equation is dimensionally correct if the dimensions of the various terms on either side of the equation are the same. Q5: Define the principle of homogeneity of dimensions. In general, physical quantity which is a ratio of two quantities of same dimension will be dimensionless. Displacement, Force, velocity etc.Īnswer: Physical quantities which do not possess dimensions are called dimensionless quantities. Planck’ Constant.Īnswer: Those physical quantities which possess dimensions but do not have a fixed value are called dimensional variables. Dimension of velocity = Displacement / time = / = Īnswer: Constants which possess dimensions are called dimensional constants. Mathematically dimensions of a physical quantity are the powers to which the fundamental quantities must be raised.Į.g.
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