Ask a Teacher

The time oscillations t of a small drop of a liquid under surface tension depends on the density d ,radius r and surface tension s.Dimensionally derive the relation between time and the given quantities

Time of oscillation,

Writing dimensions of both the sides, we have,

Comparing the powers of M,L and T on both sides, we have,

                  a + c = 0 ________ (1)

                  - 3a + b = 0 _________ (2)

                   - 2 c = 1 __________ (3)

Solving eqn (1) , (2) and (3) , we get

a = ½ , c = -1/2 , b = 3/2

Putting the valued in t