Question

The frequency v of an oscillating drop may depend upon radius R of the Drop density of liquid and surface tension S of the liquid deduce the formula dimensionally

Answer 1

Answer:

hope this answer helps.

Answer 2

Answer: n = k* sqrt(S/(p*r^3))

Explanation:

The study of the relationship between the perceived value with the help of magnitude and units of measurement is called quantitative analysis. Dimensional analysis is important because it keeps the units consistent, which helps us to do mathematical calculations smoothly.

The Homogeneity principle states that the dimensions of each term of the sum in both sides must be the same. This system is useful because it helps us to convert units from one form to another. To illustrate the point, let us consider the following example:

Dimensional analysis for formula of frequency of oscillating liquid drop.

r= radius = [L].

d= p= density = [M ][L^-3]

S = Surface Tension = [M T^-2]

n = frequency = k* r^a * p^b * S^c.

So [T^-1] = [M^b+c] [L^a-3b] [T^-2c]

Equating powers: we get

b + c = 0

a-3b = 0

-2c = -1

a = -3/2.

b= -1/2.

c=1/2.

Answer: n = k* sqrt(S/(p*r^3))

Or n = k* sqrt (S/m).

m = mass of the drop.

#SPJ2