Given the following quantities, density, acceleration due to gravity, velocity and force.find the different powers to which the quantities can be raised for their products to be dimensionless
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Answer:
The dimension of any physical quantity expresses its dependence on the base quantities as a product of symbols (or powers of symbols) representing the base quantities. (Figure) lists the base quantities and the symbols used for their dimension. For example, a measurement of length is said to have dimension L or L1, a measurement of mass has dimension M or M1, and a measurement of time has dimension T or T1. Like units, dimensions obey the rules of algebra. Thus, area is the product of two lengths and so has dimension L2, or length squared. Similarly, volume is the product of three lengths and has dimension L3, or length cubed. Speed has dimension length over time, L/T or LT–1. Volumetric mass density has dimension M/L3 or ML–3, or mass over length cubed. In general, the dimension of any physical quantity can be written as