Find the dimensions of (i) force (ii) surface tension and (iii) momentum in terms of frequency, velocity and density as fundamental units.

Find the dimensions of (i) force (ii) surface tension and (iii) moment

1.	Find the dimensions of (i) force (ii) surface tension and (iii) momentum in terms of frequency, velocity and density as fundamental units.
Answer» SOLUTION :Frequency `n=T^(-1),T=1/n` Velocity `v=LT^(-1),L=vT=v/n` Density `d=ML^(-3),M=dL^(3)=(dv^(3))/(n^(3))` (i) Force `=MLT^(-2)=(dv^(3))/(n^(3))xxv/nxxn^(2)=(dv^(4))/(n^(2))` (ii) SURFACE tension `=MT^(-2)=(dv^(3))/(n^(3))xxn^(2)=(dv^(3))/n` (iii) Momentum `=MLT^(-1)=(dv^(3))/(n^(3))xxv/nxxn=(dv^(4))/(n^(3))`