Question

A ball is dropped from a height h. If falls on the liquid surface. Its velocity does not change when it enters in the liquid, find height h in terms of r = radius of the ball, « = density of the liquid. p = density of ball. n = coefficient of viscosity and g = acceleration due to gravity:

Answer 1

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Answer 2

A ball is dropped from a height h. If falls on the liquid surface. Its velocity does not change when it enters in the liquid.

To find : The height in term of r, σ , ρ , η and g

solution : first find terminal velocity,

weight of ball, W = mg

= 4/3 πr³ρg

weight of medium displaced, F = 4/3 πr³σg

if v is the terminal velocity then from Stoke's law, upward viscus drag is given by, Fv = 6πηrv

when body attains terminal velocity,

W = F + Fv

⇒4/3 πr³ρg = 4/3 πr³σg + 6πηrv

⇒v = 2r²(ρ - σ)g/9η

now after falling through h, velocity of body should be equal to terminal velocity.

i.e., velocity of body = terminal velocity

⇒√(2gh) = 2r²(ρ - σ)g/9η

⇒h = 2r⁴(ρ - σ)²g/81η²

Therefore the correct option is (1)