A small spherical ball of radius 0.1 mm and density 104 kg m ⁻³ falls… | JEE Main 2022 (29 Jun, Shift 2)

Q42JEE Main 2022 · 29 JUN · SHIFT 2Difficult

Terminal Velocity

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 = 10 ms ${}^{-2}$ , viscosity of water = 1.0 $\times$ 10 $-$ 5 N-sm ${}^{-2}$ ).

Numerical answer type. Work it out, then open the answer.

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Answer: 20

Velocity just before entering = terminal velocity in water: $\sqrt{2gh} = \dfrac{2r^2(\rho - \sigma)g}{9\eta}$ .
$r = 10^{-4}\text{ m}$ , $\rho = 10^4$ , $\sigma = 10^3\text{ kg m}^{-3}$ , $\eta = 10^{-5}\text{ N s m}^{-2}$ .
$v_t = \dfrac{2\times10^{-8}\times9\times10^{3}\times10}{9\times10^{-5}} = 20\text{ m/s}$
$h = \dfrac{v_t^2}{2g} = \dfrac{400}{20} = 20\text{ m}$

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Terminal Velocity question from JEE Main 2022 (29 Jun, Shift 2)

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