Q.

A small spherical ball of radius 0.1 mm and density 104 kg m-3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be________m

(Given, g=10ms2, viscosity of water =1.0×105Nsm2)

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answer is 20.

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Detailed Solution

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Speed after falling through height h Should be equal to terminal velocity 
2gh=29r2(dρ)gη 2gh=29108(100001000)×10105 2gh=29×1089×104105=202×10×h=400h=20m

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A small spherical ball of radius 0.1 mm and density 104 kg m-3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be________m(Given, g=10ms−2, viscosity of water =1.0×10−5N−sm−2)