Taking force, length, and time as fundamental quantities, find the dimensional formula for the density.
1 Answer
Solution:
The physical relationship of density (D) is given as:
\(D=\frac{Mass}{Volume}\)
\(=\frac{Force/Acceleration}{Volume}\)
\(=\frac F{a\times V}\)
Dimension of F = [F]
Dimension of acceleration (a) = [LT-1]
Dimension of volume,
\(V=\left[L^3\right]\)
\(=\frac{\left[F\right]}{\left[LT^{-2}\right]\left[L^3\right]}\)
\(=\left[FL^{-4}T^2\right]\)
Hence, the dimensions of D are 1 in F, -4 in L and 2 in T ie, [F L-4 T2]
Things to remember from Physical Quantities
- Dimension of a physical quantity is the power to which the fundamental units must be raised, in order to represent it.
- The dimension of mass is denoted as [M],
the dimension of length is denoted as [L],
the dimension of time is denoted as [T],
the dimension of temperature is denoted as [K],
the dimension of electric current is denoted as [A],
the dimension of luminous intensity is denoted as [cd] and
the dimension of substance is denoted as [mol] - The expression which shows how and which of the base quantities represent the dimensions of a physical quantity is called the dimensional formula
- The dimensional equation can be obtained from the equation representing the relations between the physical quantities.
- Angle is a dimensionless physical quantity.
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