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Reference Notes
Dimensional Formula of Some Physical Quantities
Unit: Units and Measurement
Science | Physics Class 11
Dimensional formula of physical quantity can only be written when its relation with other physical quantities is known. Some of the physical quantities with the dimensional formula are given below:
| S.No. | Physical Quantity | Relation with other Physical Quantities | Dimensional formula | SI-Unit |
| 1. | Area | length × breadth | [L] × [L] = [M0L2T0] | m2 |
| 2. | Volume | length × breadth × height | [L] × [L] × [L] = [M0L3T0] | m3 |
| 3. | Density | $latex \frac{\ mass}{\ volume}&s=3 $ | $latex \frac{\ [M]}{\ [L^{3}]} = [ML^{-3}T^0]&s=2 $ | kg m-3 |
| 4. | Speed or Velocity | $latex \frac{\ distance}{\ time}&s=3 $ | $latex \frac{\ [M]}{\ [L^{3}]} = [M^0LT^{-1}] &s=2 $ | m s-1 |
| 5. | Acceleration | $latex \frac{\ velocity}{\ time}&s=3 $ | $latex \frac{\ [L T^{-1}]}{\ [T]} = [M^0LT^{-2}] &s=2 $ | m s-2 |
| 6. | Momentum | mass × velocity | [M] × [L T-1] = [M L T-1] | kg m s-1 |
| 7. | Force | mass × acceleration | [M] × [L T-2] = [M L T-2] | N (newton) |
| 8. | Pressure | $latex \frac{\ force}{\ area}&s=3 $ | $latex \frac{\ [M L T^{-2}]}{\ [L^2]} = [M L^{-1} T^{-2}] &s=2 $ | N m-2 or Pa (pascal) |
| 9. | Work | force × distance | [M L T-2] × [L] = [M L2 T-2] | J (joule) |
| 10. | Energy (Mechanical, heat, light, etc) | work | [M L2 T-2] | J |
| 11. | Power | $latex \frac{\ work}{\ time}&s=3 $ | $latex \frac{\ [M L^2 T^{-2}]}{\ [T]} = [M L^2 T^{-3}] &s=2 $ | W (watt) |
| 12. | Gravitational Constant(G) | $latex \frac{\ force \times (distance)^2}{\ (mass)^2}&s=3 $ | [M-1 L3 T-2] | N m2 kg-2 |
| 13. | Impulse | force × time | [M L T-2] × [T] = [M L T-1] | N s |
| 14. | Surface tension | $latex \frac{\ force}{\ length}&s=3 $ | $latex \frac{\ [M L T^{-2}]}{\ [L]} = [M L^0 T^{-2}] &s=2 $ | N m-1 |
| 15. | Coefficient of viscosity | $latex \frac{\ force}{\ area \times velocity gradient}&s=3 $ | [M L-1 T-1] | daP (decapoise) |
| 16. | Angle | $latex \frac{\ arc}{\ radius}&s=3 $ | Dimensionless | rad |
| 17. | Moment of inertia | mass × (distance)2 | [M L2 T0] | kg m2 |
| 18. | Angular momentum | moment of inertia × angular velocity | [M L2] × [T-1] = [M L2 T-1] | Kg m2 s-1 |
| 19. | Torque or couple | force × perpendicular | [M L T-2] × [L] = [M L2 T-2] | N m |
| 20. | Frequency | $latex \frac{\ 1}{\ second}&s=3 $ | [T-1] | Hz |
2 Comments
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Tysm for having such good responses