Question

Calculate the dimensions of force and impulse taking velocity, density and frequency as the basic quantities

Answer 1

Let we denote velocity=v, density=d, frequency=f
We have Force=[MLT^-2]
Let
MLT^-2=v^ad^bf^c
》MLT^-2=[LT^-1]^a[ML^-3]^b[T^-1]^c
》MLT^-2=M^bL^a-3bT^-a-c
On comparing the exponents of both sides
》b=1____________(1)
》a-3b=1_________(2)
》a=4
》-a-c=-2________(3)
》c=-2
Hence dimension of force is
[F]=v⁴d f^-2