Dimensions of a physical quantity are the powers to which fundamental quantities are to be raised to represent the quantity. The basic quantities with their symbols in square brackets are as follows:
$$[Length]=[L]$$
$$[Mass]=[M]$$
$$[Time]=[T]$$
$$[Temperature]=[K]or[\Theta]$$
$$[Current]=[A]0r[I]$$
$$[No.of Moles]=[N]$$
It is the expression which shows how and which fundamental quantities are used in the representation of a physical quantity.
1) Velocity [M^{0} L^{1} T^{-1}]
2) Acceleration [M^{0} L^{1} T^{-2}]
3) Force [M^{1} L^{1} T^{-2}]
4) Energy [M^{1} L^{2} T^{-2}]
5) Power [M^{1} L^{2} T^{-3}]
6) Momentum [M^{1} L^{1} T^{-1}]
7) Pressure [M^{1} L^{-1} T^{-2}]
It is the equation obtained by equating a physical quantity with its dimensional formula.
1) Velocity [V] = [M^{0} L^{1} T^{-1}]
2) Acceleration[a] = [M^{0} L^{1} T^{-2}]
3) Force [F] = [M^{1} L^{1} T^{-2}]
4) Energy [E] = [M^{1} L^{2} T^{-2}]
5) Power [P] = [M^{1} L^{2} T^{-3}]
6) Momentum [P] = [M^{1} L^{1} T^{-1}]
7) Pressure [P] = [M^{1} L^{-1} T^{-2}]
Dimensional Formulas of Some Physical Quantities
S.N | Physical quantity | Relation with other physical quantities | Dimensional formula | SI-unit |
1. | Volume | length× breadth× height | [L] ×[L] ×[L]= [M^{0}L^{3}T^{0}] | m^{3} |
2. | Velocity or speed | \(\frac{distance}{time}\) | = [M^{0}L^{0}T^{-1}] | ms^{-1} |
3. | Momentum | mass × velocity | [M] × [LT^{-1}]= [MLT^{-1}] | kgms^{-1} |
4. | Force | mass × acceleration | [M] × [LT^{-2}]= [MLT^{-2}] | N (newton) |
5. | Pressure | \(\frac{force}{area}\) | =[ML^{-1}T^{--2}] | Nm^{-2} or Pa (pascal) |
6. | Work | force × distance | [MLT^{-2}] ×[L]= [ML^{2}T^{-2}] | J (joule) |
7. | Energy | Work | [ML^{2}T^{-2}] | J (joule) |
8. | Power | \(\frac{work}{time}\) | =[ML^{2}T^{-3}] | W (watt) |
9. | Gravitational constant | \(\frac{force \times (distance)^2}{(mass)^2}\) | [M^{-1}L^{3}T^{-2}] | Nm^{2}kg^{-2} |
10. | Angle | \(\frac{arc}{radius}\) | Dimensionless | rad |
11. | Moment of inertia | mass × (distance)^{2} | [ML^{2}T^{0}] | Kgm^{2} |
12. | Angular momentum | moment of inertia × angular velocity | [ML^{2}T^{0}] × [T^{-1}]= [ML^{2}T^{-1}] | Kgm^{2}s^{-1} |
13. | Torque or couple | force × perpendicular distance | [MLT^{-2}] ×[L]= [ML^{2}T^{-2}] | Nm |
14. | Coefficient of viscosity | \(\frac{force}{\text {area} \times \text {velocity gradient}}\) | [ML^{-1}T^{-1}] | Dap (Dacapoise) |
15. | Frequency | \(\frac{1}{second}\) | [T^{-1}] | Hz |
It states that “The dimensions of fundamental quantities on a left-hand side of an equation must be equal to the dimensions of the fundamental quantities on the right-hand side of that equation.”
Physical quantities can be categorized into four types. They are:
.
The dimensional formula of universal constant is ______.
[M^{-1}L^{3}T^{-3}]
[M^{-1}L^{3}T^{-2}]
[M^{-2}L^{3}T^{-2}]
[M^{-1}L^{2}T^{-2}]
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Sep 29, 2017
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Shishir Aryal
I didn't understand the definition of dimension, Can you explain ?
Mar 30, 2017
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