Dimensions of Volume: Dimensional Formula and Derivation - Testbook.com
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What is the Dimensional Formula of Volume?
Let's delve into the dimensional formula of volume.
The formula is expressed as:
[M 0 L 3 T 0 ]
Here's what each symbol represents:
- M stands for Mass
- L denotes Length
- T signifies Time
How is it derived?
The calculation of volume (V) involves multiplying Length, Breadth, and Height, as shown in equation (1).
Volume (V) = Length × Breadth × Height . . . . (1)
The dimensional formula of length is [M 0 L 1 T 0 ] . . . . (2)
By substituting equation (2) into equation (1), we get:
Volume = Length × Breadth × Height
Or, V = [M 0 L 1 T 0 ] × [M 0 L 1 T 0 ] × [M 0 L 1 T 0 ] = [M 0 L 3 T 0 ]
Thus, the dimensional representation of volume is [M 0 L 3 T 0 ].
Explore Other Dimensional Formulas:
- Dimensions of Surface Tension
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Frequently Asked Questions
What is the dimensional formula of volume?
The dimensional formula of volume is [M^0 L^3 T^0], where M represents mass, L stands for length, and T denotes time.
How is the dimensional formula of volume derived?
The dimensional formula of volume is derived from the formula of volume, which is Volume (V) = Length × breadth × height. The dimensional formula of length is [M^0 L^1 T^0]. On substituting this in the volume formula, we get the dimensional formula of volume as [M^0 L^3 T^0].
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