Question

Define dimensional formula. What are the uses of dimensional analysis ?

Deduce the dimensional formula for

(a) Pressure

(b) Power​

Answer 1

The dimensional equations have got following three uses: To check the correctness of a physical equation. To derive the relation between different physical quantities involved in a physical phenomenon. To change from one system of units to another.

Pressure=M1 L-1 T -2

Power=kg⋅m2⋅s−3

Answer 2

Answer: Dimensional Formula is the expression which shows how and which of the base quantities represent the dimensions of a  physical quantity.

Uses/Applications of Dimensional Analysis: 1. Checking Dimensional Consistency of equations

• A dimensionally correct equation must have same dimensions on both sides of the equation.

•    A dimensionally correct equation need not be a correct equation but a dimensionally incorrect equation is always wrong. It can test dimensional validity but not find exact relationship between the physical quantities.

2. Deducing relation among physical quantities

• To deduce relation among physical quantities, we should know the dependence of one quantity over others (or independent variables) and consider it as product type of dependence.

•    Dimensionless constants cannot be obtained using this method.

Dimensional Formula for: (a) Pressure= Force = Mass x Accelaration

                                                                  Area                Area

= Mass x Distance = Mass x Length =       M.L   = ML = ML. L^-2T^-2

    Area x Time^2     Length x Time^2       L^2.T^2     L^2T^2

= ML^-1T^-2.

(b) Power= Work = Force x Distance = Force x Length = MLT^-2. L

                 Time              Time                      Time                     T

= ML^2T^-2 = ML^2T^-2. T^-1 = ML^2T^-3.

        T

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