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It two physical quantities a and b are r...

It two physical quantities a and b are related by the equation a = kb where k is dimensionless constant, then the principle of dimensional homogeneity demands that a and b have the same dimension. However the proportionality constant k cannot be determined by dimensional analysis only. It may at most be written that a `prop` b if a and b are of the same dimension.
Time period (T) of oscillation of a liquid drop depends on its radius r the density `rho` and the surface tension `sigma` of the liquid. Then T is proportional to

A

`sqrt((rhor^(2))/(sigma))`

B

`sqrt((r^(2))/(rhosigma))`

C

`sqrt((r^(3)rho)/(sigma))`

D

`sqrt((rhosigma)/(r^(3)))`

Text Solution

Verified by Experts

The correct Answer is:
C
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