Question

After being deformed, a spherical drop of liquid will execute periodic vibrations about its spherical shape. Using the method of dimensions, obtain an expression for the frequency of these vibrations in terms of the related physical quantities.

a) f = √T/rho/D
b) f = √rho/T/D
c) f = √T ⋅ rho/D
d) f = √D/rho/T

Answer 1

The correct expression for the frequency of the vibrations of a deformed spherical droplet of liquid is f = √T/rho/D. Hence the correct answer is option A

Step-by-step explanation:

To obtain an expression for the frequency of the vibrations of a deformed spherical drop of liquid using the method of dimensions, we need to identify the relevant physical quantities that affect the frequency. Based on the given options, the correct expression for the frequency is: f = √T/rho/D. Here's a step-by-step explanation:

1. T: represents the surface tension of the liquid, which characterizes how much the droplet resists deformation.
2. rho: represents the density of the liquid, which affects the inertia of the droplet.
3. D: represents the diameter of the droplet, which determines the overall size of the droplet.

By using the method of dimensions, we can determine how these physical quantities combine to determine the frequency of the vibrations. The expression f = √T/rho/D captures the relation between surface tension, density, and diameter in determining the frequency of the vibrations.

Hence the correct answer is option A