Dimensions :
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 – Mcqs 
Units & Dimensions – Notes 
Units & Dimensions – Interview Questions and Answers 
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