Question

The frequency (V) of an oscillatingj drop may depends upon radius (r ) of the drop density `(rho)` of liquid and the surface tension (S) of the liquid. Deduce of formula dimensionally.

Answer 1

Correct Answer - `v = k sqrt((S)/(rho r^3))`
Let `v = k r^a rho^b s^c….(i)`
`[M^0L^0T^(-1)] = L^a(ML^(-3))^b (MT^(-2))^c`,
`[M^0L^0T^(-1)] = M^(b+c) L^(a -3b) T^(-2a)`
`:. b + c = 0 …(iii)`
a-3b = 0 ….(iii)
`-2c = -1, :. C =(1)/(2) `
From (ii),` b = -c =-(1)/(2)`
from (iii), `a =3b =-(3)/(2)`
Put in (i) to get the required formula.