In an experiment to verify Stoke's law, a small spherical ball of radius r and density ρ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value…

Question

In an experiment to verify Stoke's law, a small spherical ball of radius r and density ρ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to (ignore viscosity of air)

Accepted Answer

(1) r⁴. Idea: the two speeds are set equal, and h follows from free fall. Terminal velocity in water: vₜ=(2r²(ρ-σ)g)/(9η)∝ r². Speed after falling h in air: v=√2gh. Setting v=vₜ: √2gh∝ r². Squaring both sides: 2gh∝ r⁴, so h∝ r⁴. The squaring is the whole question: the radius enters the terminal velocity squared, and the free-fall relation squares it again.

Step-by-step solution

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