A small spherical ball of radius 0.1 mm and density 10^4 kg m^(-3) falls freely under gravity through a distance h before entering a tank of water…

Question

A small spherical ball of radius 0.1 mm and density 10^4 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=10 m s^(-2), viscosity of water =1.0×10^(-5) N‐s m^(-2) ).

MARKS Content Team · Accepted Answer

Correct answer: 20. Using equation of motion, v^2=u^2+2as v^2=0+2-g-h ⇒v^2=2gh Initial velocity of ball is v=√2gh=√20h. If after entering the water this velocity does not change, then this value should be equal to the terminal velocity. Then, √2gh=2/9(r^2ρ-σg)/(η), here, ρ is density of ball, σ is density of water and η is viscosity. ⇒√20h=2/9(0.1×10-3^210^4-10^310)/(1×10^(-5))⇒√20h=2/9(10^(-8)10-110^3×10)/(1×10^(-5)) ⇒20h=400 ∴h=20 m

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