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← JEE Main 2022 · 29 Jun · Shift 2
PhysicsInteger+4 / -1Question 52 of 90

JEE Main 2022 · 29 Jun · Shift 2, Physics question 52

A small spherical ball of radius 0.1 mm and density 10410^4 kg m−3^{-3} falls freely under gravity through a distance hh 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 hh will be ______ m

(Given g=10g=10 ms−2^{-2}, viscosity of water =1.0×10−5=1.0\times10^{-5} N-sm−2^{-2}).

Answer and worked solution

Official answer: 20

Terminal speed in water (effective density 104−10310^4-10^3): v=2r2(ρ−σ)g9η=2×10−8×9000×109×10−5=20v=\dfrac{2r^2(\rho-\sigma)g}{9\eta}=\dfrac{2\times10^{-8}\times9000\times10}{9\times10^{-5}}=20 m s−1^{-1}.

Free fall. h=v22g=20h=\frac{v^2}{2g}=20 m.

Answer: 20