derive the dimensional formulae of area
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Answer:
The dimensional formula of area is [L2] as its SI unit is m2.
Area is the quantity that expresses the extent of a two-dimensional figure or shape or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object.
Area (A) = Length × breadth . . . . (1)
Area (A) = Length × breadth . . . . (1)The dimensional formula of length = [M0 L1 T0] . . . . (2)
Area (A) = Length × breadth . . . . (1)The dimensional formula of length = [M0 L1 T0] . . . . (2)On substituting equation (2) in equation (1) we get,
Area (A) = Length × breadth . . . . (1)The dimensional formula of length = [M0 L1 T0] . . . . (2)On substituting equation (2) in equation (1) we get,Area = Length × breadth
Area (A) = Length × breadth . . . . (1)The dimensional formula of length = [M0 L1 T0] . . . . (2)On substituting equation (2) in equation (1) we get,Area = Length × breadthOr, A = [M0 L1 T0] × [M0 L1 T0] = [M0 L2 T0]
Area (A) = Length × breadth . . . . (1)The dimensional formula of length = [M0 L1 T0] . . . . (2)On substituting equation (2) in equation (1) we get,Area = Length × breadthOr, A = [M0 L1 T0] × [M0 L1 T0] = [M0 L2 T0]Therefore, area is dimensionally represented as [M0 L2 T0].