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A metallic sphere of radius 1 × 10-3 m and density 1 × 104 kg | m3 enters a tank of water after a free fall through a high ‘h’ in earth’s gravitational field. If its velocity remains unchanged after entering water, determine the value of h. 

Given :-

Co-efficient of viscosity of water = 1 × 10-3 Ns | m2; g = 10m | s2; density of water = 1 × 103 kg | m3

1 Answer

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Best answer

The velocity acquired by the sphere in falling freely through a height h is V= √2gh

As per the conditions of the problem, this is the terminal velocity of sphere in water i.e

Terminal Velocity of sphere in water is :- VT = √2gh → 1)

By Stoke’s Law, the terminal velocity VT of sphere in water is given by :- 

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