![]() ![]() We can’t derive the formula having trigonometrical functions, exponential functions etc, which have no dimensions. This method does not give us any information about the dimensionless constants appearing in the derived formula, e.g. Thus by dimensional analysis, we conclude that the gravitational potential energy of a body is directly proportional to its mass, acceleration due to gravity and its height from the surface of the earth. U = Kmgh, where K is a dimensionless constant. Where K, a, b, and c are dimensionless constants. ![]() Let us assume that: − Gravitational potential energy, U, Suppose we have to find the relationship between gravitational potential energy of a body in terms of its mass ‘m’, height ‘h’ from the earth’s surface and acceleration due to gravity ‘g’, then, Then dimensional analysis can be used as a tool to find the required relation. Suppose we have to find the relationship connecting a set of physical quantities as a product type of dependence. (3) Deducing relation among the physical quantities: Find the conversion factor for expressing universal gravitational constant from SI units to cgs units. Thus knowing the conversion factors for the base quantities, one can work out the conversion factor of any derived quantity if the dimensional formula of the derived quantity is known. Let us consider one example, the SI unit of force is Newton. (2) Conversion of units: Dimensional methods are useful in finding the conversion factor for changing the units to a different set of base quantities. (i) Yes (ii) Yes (iii) No (iv) Yes (v) No. ![]() ‘F’ denotes Force and ‘a’ has dimensions of acceleration. Given: G = Gravitational constant, whose dimensions are M 1 ,M 2 and M have dimensions of mass. Which of the following equations may be correct ? However, all correct equations must necessarily be dimensionally correct. For example, the equation v 2 = u 2 + 3as is also dimensionally correct but we know that it is not actually correct. The equation v 2 = u 2 + 2as is dimensionally consistent, or dimensionally correct.Ī dimensionally correct equation may not be actually correct. This principle is called Principle of Homogeneity of dimensions. This means that we can not add velocity to force. ![]() The dimensions of all the terms in an equation must be identical. (1) Checking the correctness (dimensional consistency) of an equation: An equation contains several terms which are separated from each other by symbols of equality, plus or minus. etc.ĭimensionless Variables: These are the quantities, whose values are variable, and they do not have dimensions, e.g., angle, strain, specific gravity etc. For example, area, volume, density etc.ĭimensionless constants: These are the quantities whose values are constant, but they do not possess dimensions. For example, velocity of light in vacuum, universal gas constant etc.ĭimensional variables: These are the quantities whose values are variable, and they possess dimensions. Write the dimensions of: Impulse, Pressure, Work, Universal constant of Gravitation.ĭimensional constant: These are the quantities whose values are constant and they possess dimensions. ![]()
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