Question

t is directly proportional to √dr3/s​

Answer 1

the time of oscillation t of a small drop of a liquid under ... tension s derive the expre - Physics - TopperLearning.com ...

Answer 2

Let expression is T =  $r^{a}.S^{b}.d^{c}$

Here, r is the radius of drop, S is the surface tension and d is the Density of liquid .  

Dimension of T = [ T ]  

dimension of r = [ L ]  

dimension of S = [MT⁻²]  

dimension of d = [ ML⁻³]  

 

[ T ] = [L]^a [MT⁻²]^b [ML⁻³]^c  

[T] = [L]^(a -3c) [M]^(b + c) [T]^(-2b)]  

Compare both sides,  

b = -1/2 , c = 1/2 and a = 3c = 3/2  

 

Hence, expression is T = r^(3/2)S^(-1/2)d^(1/2)  

e.g., $T=\sqrt\frac{r^{3}d}{s}$

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