Question

Time period of oscillation of rain drop depends on surface tension (S), density (p) and radius (1). Then time period (T) is​

Answer 1

Answer:

Here is your answer

Explanation:

Given that,

Time Period (T) depends upon Tension (S), Density (ρ) and radius (r)

We need to find Time Period (T)

Idea:

To solve this problem the best method is dimensional analysis so that we can find whether which is constant and which is varying.

Solution:

T = K (Sᵃ rᵇ ρˣ)  {Let us assume}

Now let us use the dimensional analysis,

M⁰L⁰T¹ =R(MT⁻²)⁻²(L)ᵇ(ML⁻³)ˣ

Now let us compare powers

$0 = a +x ---->1$

$0 = b-3x ---->2$

$1 = -2a ---->3$

From 3rd equation,

a = -1/2

From 2nd equation,

b = 3x

By solving 1 & 2 we get

$X = \dfrac{1}{2}$

$B= \dfrac{3}{2}$

By applying in equation we get,

$T = K \dfrac{r\frac{3}{2} p\frac{1}{2} }{r^2}$

By taking 1/2 common we can square the inside term,

$T = K\sqrt{\dfrac{r^3p}{s} }$

This is your required time period .

Hope it helps