Dimensions – Units and Measurement

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Dimensions of any physical quantity are those powers to which the fundamental quantities are raised to express that quantity. The expression of a physical quantity in terms of its dimensions, is called its dimensional formula.

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Dimensions – Units and Measurement

Dimensional Formula of Some Physical Quantities

S.No. Physical Quantities Dimensional Formula MKS Units
1. Area [L2] m2
2. Volume [L3] m3
3. Velocity [LT-1] ms-1
4. Acceleration [LT-2] ms-2
5. Force [MLT-2] Newton (N)
6. Work energy [ML2T-2] joule (J)
7. Power [ML2T-3] J s-1 or W (watt)
8. Pressure or stress [ML-1T-2] Nm-2
9. Linear momentum or impulse [MLT-1] Kg ms-1
10. Density [ML-3] Kg ms-3
11. Strain dimensionless unitless
12. Modulus of elasticity [ML-1T-2] Nm-2
13. Surface tension [MT-2] Nm-1
14. Velocity gradient [T-1] s-1
15. Coefficient of viscosity [ML-1T-1] Kg ms-1 s-1 
16. Gravitational constant [M-1L3T-2] Nm2Kg2
17. Moment of inertia [ML2] Kg-m2
18. Angular velocity  [T-1] rad/s
19. Angular acceleration  [T-2] rad/s2
20. Angular momentum [ML2T-1] kg m2s-1
21. Specific heat [L2T-2θ-1] kcal Kg-1K-1
22. Latent heat [L2T-2] kcal/kg
23. Planck’s constant [ML2T-1] J-s
24. Universal gas [ML2T-2θ-1] J/mol-K

Homogeneity Principle
If the dimensions of left hand side of an equation are equal to the dimensions of right hand side of the equation, then the equation is dimensionally correct. This is known as homogeneity principle.
Mathematically, [LHS] =[RHS].
Applications of Dimensions

(i) To check the accuracy of physical equations.
(ii) To change a physical quantity from one system of units to another system of units.
(iii) To obtain a relation between different physical quantities.

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units Systems of Units
Dimensions Significant Figures
Rounding off Error
Combinations of Errors