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Grade -11 (NEB) > Science Physics Dimension of Physical Quantities, Physical Quantities

What is the dimensional formula for density?

Taking force, length, and time as fundamental quantities, find the dimensional formula for the density.

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Tribhuvan University > Institute of Science and Technology > B.Sc. (CSIT)

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]

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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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