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The time period (T)of a small drop of liquid under surface tension depends on the density(d ), radius (r) and surface tension (S) .Prove that Tµ ( hint :S is force acting per unit length)

  1.      The time period (T)of a small drop of liquid under surface tension depends on the density(d ),  radius (r) 
and surface tension (S) .Prove that Tµ  ( hint :S is force acting per unit length)

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Let expression is T = 
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)
 
T = sqrt (r3d / S)

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