A water droplet starts falling from rest, from a height h and acquires the terminal speed…

Physics · JEE Main · NTA Exams — Properties of Solids and Liquids

A water droplet starts falling from rest, from a height h and acquires the terminal speed just before reaching the ground. If g (acceleration due to gravity) is assumed to be constant and radius of the drop is r, the work done by air drag is (The coefficient of viscosity of air is η)

\(\frac{4}{3} \pi r^{3} \rho_{n} g\left[\frac{2 r^{4} g}{81 \eta^{2}}\left(\rho_{n}-\rho_{a i r}\right]^{2}-h\left(1-\frac{\rho_{a i r}}{\rho_{n}}\right)\right]\)
\(\frac{4}{3} \pi r^{3} \rho_{a i r}\left[\frac{2 r^{4} g}{81 \eta^{2}}\left(\rho_{n}-\rho_{a i r}\right)^{2}-h\right]\)
\(\frac{4}{3} \pi r^{3} g\left[\frac{2 r^{4} g}{81 \eta^{2}}\left(\rho_{n}-\rho_{\text {air }}\right]^{2}-h\right]\)
\(\frac{4}{3} \pi r^{3} \rho_{n} g\left[\frac{2 r^{4} g}{81 \eta^{2}}\left(\rho_{n}-\rho_{\text {air }}\right]^{2}\right]\)

Answer

(C) 4 3 r^ 3 g [ 2 r^ 4 g 81 ^ 2 ( _ n - _ air ]^ 2 -h ]

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A water droplet starts falling from rest, from a height h and acquires the terminal speed…

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