Question

Example 32. If densitu p, acceleration due to gravity g and
frequency are the basic quantities, find the dimensions of force.

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Answer 1

Answer:

FORCE=mass*acceleration

and acceleration=velocity/time.

and velocity=distance/time

Therefore FORCE=(mass*distance)/time^2

As mass tends to M, distance tends to L, time tends to T dimensionally.

So, Dimensions of FORCE=(ML)/T^2

That is Dimensions of FORCE = [MLT^-2]

F=ma

Force equals mass times acceleration.

the dimension of mass is mass.

the dimension of acceleration can be expressed as velocity per time. and velocity can be expressed as distance per time.

Mass, Distance, Time are easy for us to measure, so those are the basic dimensions we like to use.

Force is then has the dimensions of Mass times Distance per Time per Time.

Other systems of measurement like to say that force is a basic measurement, and that mass is derived from that. in which case Mass has the dimensions of Force times Time times Time per Distance.