Dimentions

The exponent of a base quantity that enters into the expression, is called the dimension of the quantity in that base.

When a quantity is expressed in terms of the base quantities, it is written as a product of different powers of the base quantities.

Force is equal to mass times acceleration. Acceleration is change in velocity divided by time interval. Velocity is length divided by time interval. Thus,

Force = mass x acceleration

Force = mass x (velocity/time)

Force = mass x {(length/time)/time}

Force = mass x length x (time)^{-2}

Thus, the dimensions of force are 1 in mass, 1 in length and – 2 in time.

Dimensional formula of some derived quantities :

Physical quantity | Expression | Dimensional formula |

Area |
length × breadth |
[L^{2}] |

Density |
mass / volume |
[ML^{−3}] |

Acceleration |
velocity / time |
[LT^{−2}] |

Momentum |
mass × velocity |
[MLT^{−1}] |

Force |
mass × acceleration |
[MLT^{−2}] |

Work |
force × distance |
[ML^{2}T^{−2}] |

Power |
work / time |
[M L^{2}T^{−3}] |

Energy |
work |
[M L^{2}T^{−2}] |

Impulse |
force × time |
[MLT^{−1}] |

Radius of gyration |
distance |
[L] |

Pressure |
force / area |
[ML^{−1}T^{−2}] |

Surface tension |
force / length |
[MT^{−2}] |

Frequency |
1 / time period |
[T−1] |

Tension |
force |
[MLT^{−2}] |

Moment of force (or torque) |
force × distance |
[ML^{2}T^{−2}] |

Angular velocity |
angular displacement / time |
[T^{−1}] |

Stress |
force / area |
[ML^{−1}T^{−2}] |

Heat |
energy |
[ML^{2}T^{−2}] |

Heat capacity |
heat energy/ temperature |
[ML^{2}T^{-2}K^{-1}] |

Charge |
current × time |
[AT] |

Faraday constant |
Avogadro constant × elementary charge |
[AT mol^{-1}] |

Magnetic induction |
force / (current × length) |
[MT^{-2}A^{-1}] |

Units & Dimensions – Mcq |
Units & Dimensions – Notes |
Units & Dimensions – IQ |

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